The problem is:
9 guys are racing.
The favorite has a probability of 3/4 to win the race.
Each other competitor has an equal chance to win.
If it becomes known that the favorite did not win the race, what is the uncertainty of the result?
My intuition would be a conditional entropy approach H(X|Y) where X denotes the competitor and Y the information that the champion did not win. My trouble is on how to model the P(X|Y) and P(X,Y) needed to find the entropy.