If there are 3 people in a room, the probability of two of those people having THE SAME birthday is 0.008. For 4 people, it is 0.016 and for 5 people, it is 0.027.

Using the same rule of at least two people in a room of size 25, what is the probability (rounded to the nearest 1000th) of two people having THE SAME BIRTHDAY?

For the purpose of the calendar, there are 365 days in the year (Feb. 29th is counted a Mar. 1st).

Enter the answer in the following format: 0.XXX where X represents the digits of the answer.

Thanks to Triple_M_2000 and rayfil for the clarification!