Hold'em Hand Analysis

[DoctorWard]

You are heads up at the end of a tournament. You look down at your pocket cards to see Qh-3h. The flop comes 3c-Kh-Th and your opponent moves all-in and you call. Your opponent flips over 9h-9s.

He is currently ahead but you have the best of it because of your draws. There are 45 cards remaining in the deck so there are 45C2 combinations (i.e. 990 combinations) for how the turn and the river may fall. What is the probability of winning this hand? Describe and determine the probability of all situations where you could win? For example, you could win where both a K and T fell on the turn and river, and there is 3 x 3 combinations of this so you have 9/990. Account and quantify for the different ways in which you can win this hand (nb. not all ways are mutually exlcusive) and therefore, determine what is the probability of winning this hand?

Using pokenum from Sourceforge

Before the flop:
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Qh 3h 534709 31.23 1168549 68.24 9046 0.53 0.315
9s 9h 1168549 68.24 534709 31.23 9046 0.53 0.685

After the flop:
Holdem Hi: 990 enumerated boards containing 3c Kh Th
cards win %win lose %lose tie %tie EV
Qh 3h 499 50.40 491 49.60 0 0.00 0.504
9s 9h 491 49.60 499 50.40 0 0.00 0.496

See my website's Texas Holdem Odds Calculator for an online version.

[DoctorWard]

Thanks, but didn't really answer my question...
I know the answer is 499/990 however, I think this is right...

a) Any heart will win (324/990)
b) Any 3 except with a 9 (66/990)
c) Any Q except with a 9 (85/990)
d) A + J (9/990)
e) K + T (9/990)
f) J + 9 (6/990)

(a) to (f) are the mutually exclusive numbers. Can anyone confirm?