So it's about 1%, assuming uniform distribution of birthdays. Since they're not quite uniformly distributed, the actual odds of 60 people with no common birthdays is a little lower than that.
However, given the thousands of people reading HN who experienced such a classroom exercise, the odds are very good that someone like you will pipe up ;-)
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365! / ((365-60)! 365^60) = 0.0059
So it's about 1%, assuming uniform distribution of birthdays. Since they're not quite uniformly distributed, the actual odds of 60 people with no common birthdays is a little lower than that.
However, given the thousands of people reading HN who experienced such a classroom exercise, the odds are very good that someone like you will pipe up ;-)