A race track betting board has the following odds against:

Horse A 9:2

B 6:1

C 11:3

D 19:2

E 10:1

F 13:2

A bet called a "triactor" is when you name the exact order of the first 3 horses in the race. What is the probability of winning the triactor?

I have been told that odds at the race track doesn't translate from straight probabilities, but factors in the number of betters etc.

I'm treating it more as a question on probabilities.

I assumed that the question is assuming that I'll pick the horses with the top 3 probabilities to win: so C, A, and B, in that order. What I'm also assuming is that the odds/probabilities listed are for finishing first. So, I thought I'd take 3/14 and multiply by (2/11)/(1-(3/14)) since we want to know the probability that A finishes first given C is out and then do the same for B. Is this reasoning flawed?