Suppose events A and B are such that P(A intersection B) = 0.1, and P((A U B)complement) = 0.3. If P(A) = 0.2, what does P (A intersection B) given (A U B)complement equal?

Shouldn't it be 0? Given (A U B)complement has occurred, that is all events where A and B do not occur. So P (A intersection B) given this has to be 0 right? I feel like I'm overthinking it.