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.
Simple: The fact that we don't see strange things happening is bayesian evidence that we don't live in a world where that is possible.
As I already mentioned, it is probability itself which must be justified in the first place. How do you do that?