Cyc doesn't do anything Bayesian like assigning specific probabilities to individual beliefs - IIRC they tried something like that and it had the problem where nobody felt very confident about attaching any particular precise number to priors and also the inference chains can be so long and involve so many assertions that anything less than 1 probability for most assertions would result in conclusions with very low confidence levels.
As to what they actually do, there are a few approaches.
I know that for one thing, there are coarse grained epistemic levels of belief built into the representation system - some predicates have "HighLikelihoodOf___" or "LowLikelihoodOf___" versions that enable very rough probabilistic reasoning that (it's argued - I have no position on this) is actually closer to the kind of folk-probabilistic thinking that humans actually do.
Also Cyc can use non-monotonic logic, which I think is relatively unique for commercial inference engines. I'm not going to give the best explanation here, but effectively, Cyc can assume that some assertions are "generally" true but may have certain exceptions, which makes it easy to express a lot of facts in a way that's similar to human reasoning. In general, mammals don't lay eggs. So you can assert that mammals don't lay eggs. But you can also assert that statement is non-monotonic and has exceptions (e.g. Platypuses).
Finally, and this isn't actually strictly about probabilistic reasoning, but helps represent different kinds of non-absolute reasoning: knowledge in Cyc is always contextualized. The knowledge base is divided up into "microtheories" of contexts where assertions are given to hold as if they're both true and relevant - very little is assumed to be always true across the board. This allows them to represent a lot of different topics, conflicting theories or even fictional worlds - there are various microtheories used for reasoning events in about popular media franchises, where the same laws of physics might not apply.
I understand that any practical system of this kind would have to be very coarse, but even at the coarse level, does it have any kind of "error bar" indicator, to show how "sure" it is of the possibly incorrect answer? And can it come up with pertinent questions to narrow things down to a more "correct" answer?
The latter thing sounds like something Doug Lenat has wanted for years, though I think it mostly comes up in cases where the information available is ambiguous, rather than unreliable. There are various knowledge entry schemes that involve Cyc dynamically generating more questions to ask the user to disambiguate or find relevant information.