This makes assumptions such as the existence of the world and the existence of bets which a global sceptic would not believe.
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'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.