The probability of the interval

There is N random events occurring in the interval [0,T].Suppose the
occurring time is 0<=T(1)<=T(2)<=...<=T(N)<=T.The number of events N
is satisfied with Possion distribution (with Constant P
P(n=N)=p^N/N!*exp(-P)). How to get to the probability function of the
T(i+1)-T(i)

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1 7th November 10:03 liuwei99 External User Posts: 1	The probability of the interval There is N random events occurring in the interval [0,T].Suppose the occurring time is 0<=T(1)<=T(2)<=...<=T(N)<=T.The number of events N is satisfied with Possion distribution (with Constant P P(n=N)=p^N/N!*exp(-P)). How to get to the probability function of the T(i+1)-T(i)