To win, you opponent has to be incorrect with all three predictions. The first prediction has a 10/13 chance of being incorrect. The second guess has a 9/12 chance of being incorrect, because we can remove the first rank guessed as a possibility. The third guess has an 8/11 chance of being incorrect, because we can remove the first two ranks guessed as a possibility.
All three of these things would have to happen for you to win. Thus, the chances of you winning are (10/13) * (9/12) * (8/11) = 720/1716 = 41.96%.
At even money, the house edge on this bet, from your side, is 16.08% (ouch!).
This question was culled from The Book of Proposition Bets by Owen E'Shea (number 7).