Thread: Probability of finishing in first three places of a race

If we have a 10 runner horse race and we perceive the probabilities of winning the as follows...

Horse 1 35%
Horse 2 15%
Horse 3 10%
Horse 4 10%
Horse 5 10%
Horse 6 5%
Horse 7 5%
Horse 8 4%
Horse 9 3%
Horse 10 3%

how would formulate the chance of a single horse finishing either first, second or third? Or would the probabilities of winning the race not be enough?

p.s. I'm no maths expert so a dumbed down version would do if possible.

Thanks,
Adam.

you need more info
you really need to know the joint distribution of all 10, how they compete against each other.
I've seen where in baseball team A can beat team B, while team B can dominate team C
and yet C beats on A as well.