Circular arguments have no correlation with reality except by chance- you may as well make something up and believe it. It would make about as much sense.
It is correct that if skepticism is correct then there is nothing we can do. Logically speaking, since probability doesn't exist there is a probability of 100%.
For skepticism to be correct you would need to show that it's possible to be skeptic.
It's certainly possible to pretend to be skeptic but pretending to be skeptic doesn't make you any more of a skeptic than pretending to be a duck makes you a duck.
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.