I don't quite understand it. As far as I can tell, logic isn't about probability, it's about consistency. To whit:
(1) All men are mortal.
(2) Socrates is a man.
(3) Socrates is mortal.
(3) follows from (1) and (2) because the denial of (3) is inconsistent with (1) and (2). That's the definition of validity. It's not probably inconsistent with them, it flat out is inconsistent with them.
Logic deals with form, not content. It's the study of what forms of argumentation are valid, on the basis of what sorts of statements are consistent with each other. You can replace "men", "mortal", and "Socrates" in the above syllogism with anything you like, and it will still be valid (although the premises or the conclusion might not necessarily be true, but that's another matter and not one addressed by logic).
You'd have to have a very radical scepticism indeed to be able to doubt good logical reasoning, because unlike empirical or perceptual claims (the usual things that sceptics doubt) it leaves no room for doubt. Even if I doubt that I'm really sitting here - even if I think perhaps I'm dreaming or being tricked by a malicious demon - I cannot doubt the validity of the above syllogism, at least not in the same way. To doubt it I'd have to doubt all reasoning, without exception. But if I then infer anything from this doubt (e.g., the conclusion that logic can't be trusted), I'm using reasoning, and I'm no longer consistently doubting it.
Also, why would you doubt such things in the first place? Sceptical arguments usually turn on the point that things like memory or sensory perception are fallible, because we've found them to be imperfect. And there are masses of examples, e.g. the stick that is straight but looks bent when put in water, or the tower that is square but looks round from a distance, or the jaundice that makes sufferers perceive everything to be yellow (not actually true, but a frequently repeated example from, I think, Sextus Empiricus onwards). And the argument basically boils down to the claim that any source which has let us down in the past isn't entirely reliable and therefore can't be entirely trusted. But it's hard to see how this argument could be applied to logic, since you'd have to have an example of logic being wrong. Of course people sometimes make mistakes when trying to think logically, but the error is theirs, not logic's. They may think they're thinking logically but they're not.