That gives him 365 possible birthdays out of 365 days, so the probability of the first person having the "right" birthday is 365/365, or 100%. The chance that the second person has the same birthday is 1/365. To find the probability that both people have this birthday, we have to multiply their separate probabilities.
Math Forum: Ask Dr. Math FAQ: The Birthday Problem
mathforum.org/dr.math/faq/faq.birthdayprob.html
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