The belief in miracles clearly involves causal reasoning. Something unexpected happened because of supernatural intervention in the normal course of events.
It’s a funny case for Hume, though. No one ever directly experiences the supernatural causes that they believe in. At best, they’re known through their effects, the unexpected events.
Hume’s psychological theory is entirely devoted to what he regards as the normal, healthy, and natural kinds of thinking. This is so even when he reaches skeptical conclusions, as he does with causal reasoning on the basis of experience.
He clearly regards the kind of reasoning people go through when they believe in miracles as mistaken. He also offers some fragmentary explanations of their beliefs. For instance, he points out how people are motivated to believe in the wonderful and extraordinary. But he doesn’t develop anything like the theoretical apparatus that he does in sections 5 and 7 to explain the belief in miracles.
I think this throws some light on the nature of Hume’s skepticism about causal inferences. He doesn’t think they’re based on reasoning. We have just as much reason for thinking that the billiard ball will move in the expected way as we do for thinking that it will hop in the air. But he clearly thought there were better and worse ways of drawing causal inferences. The belief in miracles is far worse, by his lights, than the everyday causal inferences he had described earlier.
So how does he fit all of that together?
As a general matter, Protestants were officially committed to the doctrine that miracles had ceased after the Christian church was established. The prophets, Jesus Christ, and the disciples all performed miracles in order to establish that they represented or acted for God. Thus they accepted every miracle reported in the Bible.
(I should add that some Protestants, such as Rev. Welch and the Kings of England seemed fairly comfortable with performing miracles. King James got used to curing scrofula with the Royal Touch and Charles II was especially fond of the ceremony. The fact that it helped to establish his royal status after the English Civil War didn’t hurt.)
Protestants spent a fair amount of time challenging putative miracles in Catholic countries or by members of the Catholic church. This is evident in Archbisoph Tillotson’s sermon on the eucharist.
Hume connected the dots by applying the Protestant arguments against contemporary miracles to the miracles reported in the Bible. If we have no reason to believe in the miracles reported today, why think we have any reason to believe in the ones reported in the Bible?