Team Winners

A tournament consistent of $32$ teams plays in a round-robin style tournament. This means that every single team plays every other team exactly one time. Suppose that every team is equally skilled so that every team is equally likely to beat any other team in a given match. Each team keeps track of how many wins they have. Find the probability that every team has won a distinct number of games at the end of the tournament. The answer will be in the form $\dfrac{a!}{2^b}$ for integers $a$ and $b$, where $b$ is maximal. Find $a + b$.