Poisson process problem

alehand12

Given a poisson process Z(t) with a given rate lamda, k and m nonnegative integers and t and c real and positive numbers, calculate the probability:
P(Z(t-c)=m | Z(t)=k)

thanks

bpet

Hint: conditional on the number of jumps in a Poisson process, the jump times are uniformly distributed over the time interval.