Probability of leading at quarter time

Hi all,

I'm interested in calculating the probability that a sporting team will be leading at quarter time if the probability of the team winning the match is known. I could just have easily said "the chance of winning a nominated quarter" or some such, but for simplicity I'm just using the first quarter.

Lets assume that the sport is basketball and that an average match score is 100 points for each team. (The sport that I'm interested in probably isn't basketball but basketball is a close enough approximation). Let's also rule out idiosyncracies like running down the clock, psychological factors etc. Both teams just want to score goals. Simple :)

Lets say that team A has a 90% chance of winning the match, team B has an 8% chance and there is a 2% chance of a tie.

I'm guessing that the chance of team A winning the first quarter is about 75%. Could somebody please describe a method for calculating the correct figure in this example, which I could then apply to other examples.

I don't mind if the solution doesn't fully cater for a tie - that would be an unexpected bonus. If somebody can supply a "good enough" formula then I can factor in the probability of a tie using a best guess.