When referring to the record of team, let x,y mean a team has won x games and lost y games out of a total of x+y games played.

Suppose a team currently has a 1,1 record, having won one of its first two games. From there on the team's probability of winning its game is equal to its current proportion of wins. (For example if after 8 games their record is 5,3 they have a 5/8 chance of winning the next game.)

[1] Find the probability that the team will have a record of a,b after it has played a total of a+b games.

[2] If we know they lost their third game so they are now 1,2, again find the probability of having a record of a,b after a+b games.