Chance of winning

[Gene2x]

Here's another problem and how I analyzed it. Please tell me if I'm going about it wrong:

3 opponents (random cards), you have K4, board is T-A-K.

Analysis: Chance of anyone having an A on the flop (one on the board) is about 13%. With three opponents, there's a 40% someone has an A. There's a 17% chance anyone has any one card of a particular rank (not on board). With three to a straight on the board here, there's a 51% chance someone has a J and an 18% chance they'll get the Q for a straight by the river. Multiplying the odds of both happening gives about 9%. Same calculation for someone having a Q and hoping to hit a J.

Odds of being beat by river: 40% + 9% + 9% = about 60%. Equity is about 40%.

Now, in actuallity, there were two of the same suit on the board. So, it seems like the situation is a lot more complicated and I must be missing stuff. Software tells me my equity is 41%. So, I came close- but was it coincidence?