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The answer is 398,581/48,627,125 or approximately 0.0082.
Call the people Al, Betty, and Chuck.
The probability that Al isn't born on your birthday is 364/365. Likewise for Betty and Chuck.
These three probabilities are independent (knowing Al's birthday doesn't influence your probability for Betty), so we can find the probability that *none* of these people share your birthday by multiplying:
364/365 * 364/365 * 364/365 = 48,228,544/48,627,125.
But we want the probability that one of these people *does* share your birthday. This is exactly the negation of the event that none of them share your birthday, so the probability is one minus that;
1 - 48,228,544/48,627,125 = 398,581/48,627,125.
Another approach to this problem: there are 48,627,125 possible arrangements of these people's birthdays (365*365*365). Of these, there are (1*365*365 + 364*1*365 + 364*364*1), or 398,581, arrangements in which at least one person shares your birthday. So, the probability of that event is 398,581/48,627,125.