Maths/probability question on matchbets

Wondered if anyone could help me at all with the below?

there are 3 golfers playing together on a given round.  i can estimate that
A is 55% to beat B (45% to lose, i am ignoring draws for now)
A is 75% to beat C
B is 65% to beat C

What does this mean the chances of the winner of the 3-ball should be?  Obv it is easy to see A will be fave and C the big outsider

To win the 3 ball, A has to beat B (55%) but also be beating C.  This introduces conditional probability - ie. once A has beaten B, he's more likely to have had a good round and thus his chance of having beaten C is going to be higher than 75%.  But i cant work out by how much, otherr than by simply guessing the multiples below?

i.e  A's chances of winning 3 ball would be
55%*(some multiple, x say, of 75%)

And obv similar logic for B&C's chances.
B = 45% * (another multiple, y, of 65%)
C = 25% * (z * 35%)

Clearly i know the sum of the 3 chances must sum to 1 but this isnt enough to deduce an answer, because the 3 multiples x,y,z will take on different values.  I suspect theyll all tend to be something like 1.1-1.4, higher for the outsiders.  ie. once C has beaten A then Id expect him to be not far off 50% to have beaten B too (45% would need z to be around 1.3) 

I know that Bayes would say
P(A beats C, given A beats B) = ( P(A beats B, given A beats C)*P(A beats C) ) / P(A beats B)

But not sure that helps me as i dont know either of the conditional probabilities


Any ideas or thoughts appreciated - in particular can maths help me with this or do i have to basically find a way of guesstimating x,y,z myself?