While the math is way over my head, I learned years ago that the odds of two people sharing a birthday are about 50% for a group of 23, about 95% for a group of 50 and over 99% for a group of 60 persons.
There's tons of related math stuff on the internet, but I could not easily find the odds of three persons sharing the same birthday.
However, it was certainly a statistical oddity that three of the 25 players on the 1950 N.L. Champion Philadelphia Phillies shared the same natal anniversary.
Andy Seminick was born Sept. 12, 1920; Bubba Church on Sept. 12, 1924 and, Stan Lopata on Sept. 12, 1925.