I've been racking my brain for ages trying to solve this but I can't seem to get the last step.

The question is, given

Code:

` 0<u<t , 0<=k<=n`

Code:

`P(X(u) = t | X(t) = u) = (n choose k) (u/t)^k (1-(u/t))^(n-k)`

X(t) is a poisson process with rate lambda