I think it's mostly a founding effect - for some reason the site started out with disproportionally many hep-th people and therefore kept attracting more of them
IMO you don't need that much probability theory for introductory QM. If you know about discrete and continuous random variables and can compute expected values/moments you are essentially fine
But I think, or I believe that statistics/probability theory is important in quantum statistical mechanics. Hence why I wanted to dive in more into the subject
just having a quick look at my books, Jacobs' "Stochastic processes for physicists" chapter 1 seems like the sort of thing you are looking for (but I don't think I've ever read it)
Also the first chapter of Schwabl - stat mech. Peliti's statmech in a nutshell has a shorter appendix