In my view, you shouldn't care much about the answer to this question. The only time you should care a lot about the probabilities involved is when you are choosing a betting strategy - in this instance, you should be interested in the probability that your opponent has a higher pair before calling his all in.

But maybe you're just curious and want to know the probability before seeing all the cards on the table. In that case, the answer seems to me to depend on how many players there are (how many people were dealt two cards before it was just you vs. your opponent), and whether you are "burning" cards (laying one card aside before the flop, another before the turn, and one more before the river). I'll think about that. And maybe someone else will chime in.