Let's say there are two markets A and B. I believe market A current probability P(A) logically implies a different probability P(B) for market B than it's currently valued at.

This can happen for example if the two markets bet on the same event, or very close events, or if A implies B, etc.

Note that this does not necessarily imply that I have better knowledge than the markets about P(A) or P(B). In most cases I don't.

How do I use this knowledge to extract value from these markets?