Am I ahead?

[TJD]

I am trying to determine the best way to calculate the probability of me being ahead of N opponents on a flop.

e.g. I have A7o and 2 opponents and spike middle pair on K72r board.

It is easy to work out if anyone has AT LEAST 1 King but I also need to consider 77,22, 72 or a PP higher than 7's

I think against 1 opponent the chance of them having a K is 12.5% but this clearly understates the chance of me being behind.

It would be also fairly easy to work out for ONE opponent the probability that they have any hand that could be ahead of me.

However, I see no easy way to apply that to more than one opponent.

My instinct is to work out the probability for one to beat me and then do 1- P(they are ahead) to get their "fail to beat me" probability and raise this to the power of the number of opponents; take that from 1 and voila!

However, I have no idea whether this is correct, since the P's would clearly change for player 2 if we KNEW what player 1 had.

Any ideas?

Cheers

T