If you don't believe in the existence of the external world, then you shouldn't be worrying about the "notion of probability having a correlation with reality" in the first place. The OP presupposes the existence of the world. Do not shift the goalposts.
I never said I disbelieved in it- I'm postulating, not accepting a position. It is also worth noting that in my postulated position I was neither accepting nor rejecting the existence of said external world.
As I mentioned, this argument started out on the basis of trying to figure out if something could be known without assumptions that could not themselves be justified. If assumptions are necessary to know anything, it means that we effectively believe on religious-style faith.
I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.