Probability's hard to teach. You can give informal statements and kind of wave your hands at the underlying theory, or you can give a rigorous well-founded treatment that's intellectually satisfying. But the rigorous foundation uses math that's a step or two beyond what undergraduate math majors learn. It's not necessarily harder than what math majors see, but it's a ton of extra material to teach, when the payoff is that you can now (after half a year) prove that the conditional probability is well-defined as
Pr(A | B) = Pr(A and B) / Pr(B)
instead of just telling it to students and drawing a few diagrams that drive the point home.
But I think it's more pragmatic than ad hoc. Any deep theory of probability that doesn't deliver
Pr(A | B) = Pr(A and B) / Pr(B)
is basically useless since that's how random phenomena seem to behave in real life. Having a deeper theory is useful because it allows you to derive other implications of that theory and makes certain calculations much easier. But if the theory disagrees with phenomena that we want to model, that can be a problem.
Pr(A | B) = Pr(A and B) / Pr(B)
instead of just telling it to students and drawing a few diagrams that drive the point home.
But I think it's more pragmatic than ad hoc. Any deep theory of probability that doesn't deliver
Pr(A | B) = Pr(A and B) / Pr(B)
is basically useless since that's how random phenomena seem to behave in real life. Having a deeper theory is useful because it allows you to derive other implications of that theory and makes certain calculations much easier. But if the theory disagrees with phenomena that we want to model, that can be a problem.