[irchans]

I don't really understand your question, but I can ask a different question that has the same answer.

If
1) there were two possible hands on the river,
2) the probability of you getting the top hand is P1,
3) the probability of your opponent getting the top hand is P2, and
4) those probabilities are independent,
then the probability of you winning is

P = P1 (1-P2).