Probability of arrival n happens at time t in Poisson

Suppose there's a birth process which is a Poisson process with
parameter b.
The birth process generates a sequence of integer numbers following a
sequence (0,1,2,3,..) during a time interval T.
Knowing that in time T the process generated N numbers, what is the
probability that number n<=N was generated precisely at time t (where t
<=T)?
Note that in the birth process, the probability that it generates a
number in a time slot delta_t is given by b*delta_t.

I expect the solution to be e^-(b*t)*b*delta_t, but i'm not 100% sure.

Thanks!

.

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