Odds of two people having same birthday

[DVO]

This doesn't sound right. Read it in an excellent book on Warren Buffett, who of course is very proficient in the area of probability.

In the book, Buffett is in a room with 25 other people, and bets a friend that among this group will be at least one shared birthday. Buffett wins the bet and informs his friend the odds were in favor of it.

Doesn't sound right to me at all. Any thoughts? calculations?