10-7 is largely dedicated to the factors that impact the veracity given to testimony that is probably shared universally by most people. 10-8 however establishes a principle that underlies the rest of Hume’s argument, so I think it merits close attention. The bolding, italics, and underlining, in the following quote is mine:Hume wrote:This contrariety of evidence, in the present case, may be derived from several different causes; from the opposition of contrary testimony; from the character or number of the witnesses; from the manner of their delivering their testimony; or from the union of all these circumstances. We entertain a suspicion concerning any matter of fact, when the witnesses contradict each other; when they are but few, or of a doubtful character; when they have an interest in what they affirm; when they deliver their testimony with hesitation, or on the contrary, with too violent asseverations. There are many other particulars of the same kind, which may diminish or destroy the force of any argument, derived from human testimony.
Suppose, for instance, that the fact, which the testimony endeavours to establish, partakes of the extraordinary and the marvellous; in that case, the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual. The reason, why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive à priori, between testimony and reality, but because we are accustomed to find a conformity between them. But when the fact attested is such a one as has seldom fallen under our observation, here is a contest of two opposite experiences; of which the one destroys the other, as far as its force goes, and the superior can only operate on the mind by the force, which remains. The very same principle of experience, which gives us a certain degree of assurance in the testimony of witnesses, gives us also, in this case, another degree of assurance against the fact, which they endeavour to establish; from which contradiction there necessarily arises a counterpoize, and mutual destruction of belief and authority.
I should not believe such a story were it told me by Cato; was a proverbial saying in Rome, even during the lifetime of that philosophical patriot. The incredibility of a fact, it was allowed, might invalidate so great an authority.
What the italicized “à priori” means here is a distinction between two types of knowledge. Knowledge that is a priori means that it is knowledge that is obtained without experience. Traditionally what has constituted a paradigmatic examples of a priori knowledge has been mathematics and geometry; we know Pythagoras's theorem is true not because we’ve gone out and confirmed it by measuring a bunch of right triangles, but because it can be proven by referencing just the principle relations involved in the theorem itself. By contrast, “a posteriori” knowledge comes after experience and if mathematics and geometry are paradigmatic examples of a priori knowledge then physics and chemistry would be paradigmatic examples of a posteriori knowledge. If you are forming hypotheses and then conducting experiments to confirm or disconfirm that hypothesis, then modifying your hypothesis in light of your experimentation, you are dealing in a posteriori knowledge.David Hume wrote:The reason, why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive à priori, between testimony and reality, but because we are accustomed to find a conformity between them.
Take a second look at the bolded section of the above quote, what is Hume saying? I would submit that when Hume writes “any connexion, which we perceive à priori” he is referencing an idea that philosophers today call the “Principle of Sufficient Reason” (hereafter: PSR). Now there is a lot to be said about this principle and it was much discussed between the so-called “Rationalist” philosophers like Spinoza and Leibniz who preceded Hume. We don’t need to cover much of it other than the core element at the center of the principle which I would roughly characterize for this thread as “every event has a cause”.
You might recognize the PSR as constituting one of the premises that make up William Lane Craig’s kalam cosmological argument. Hume disputes that we can know the PSR is true a priori and he disputes that we could learn the truth of the PSR a posteriori. The SEP has a succinct paragraph that quickly captures the spirit of Hume’s objection:
Going back to the underlined portion we read that it isn’t a metaphysical connection witnesses have to supposed events that makes their testimony believable, but their conformity with our experiences. This is the fundamental principle that allows Hume’s arguments against miracles to operate. In practice it gives witness testimony a secondary role in evidential assessment similar to how secondary sources are given less credence than primary sources are in historical studies.SEP wrote:Hume’s critique of causation presents an important challenge to the PSR. In his Treatise of Human Nature (I, 3, 3) Hume considers several arguments which attempt to prove the “general maxim in philosophy, that whatever begins to exist, must have a cause” and finds all of them wanting. Hume argues that since the ideas of cause and its effect are evidently distinct, we can clearly conceive or imagine an object without its cause. He takes the separability of the two ideas to show that there is no necessary conceptual relation between the ideas of cause and effect insofar as conceiving the one without the other does not imply any contradiction or absurdity.
Reading the rest of the paragraph gives us a clearer picture of this operation. When witness testimony is given and it conforms with what we already know by experience, a sort of equilibrium is struck between the testimony and our experience:

When the testimony of witnesses contradicts what we know from experience, the evidentiary weight given to the testimony is reduced and what is known to us already is given more credence.

The last paragraph is Hume providing an example of this principle from classical antiquity, where even the most respected of persons giving a testimony could not override something that was considered obviously known.