I cheerfully plead guilty on all charges.
I am not a skeptic. I am unbothered by any logical circularity in my belief in objective reality. I see no reason to worry about a belief I am incapable of believing.
Honestly, I can't quite picture what it would be like to worry about such things, let alone believe them. If the universe doesn't exist, there's nothing you can do about it, so why waste energy thinking about the possibility?
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%.
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.