[pococurante]

There are 2,598,960 possible 5-card combinations. 59,280 of those include 3 of a kind. We can toss out the 4560 combinations of trip aces, and the 4560 trip deuces, leaving you with 50160 live hands so far.

Given trips, there is a 8/49 chance that your next card will either be 1 below or one above. Then your next card has a 4/48 chance of completing the hand that you want.

Results: There are 682.5 combinations out of 2,598,960 that will win. Since there are no half-cards in poker, the answer is wrong, probably because the card combination numbers I looked up were off... this number should be very close though.