I think you mean what is the probability that their birthdays will be in different months.
It doesn't matter what month the first person's birthday is in. The second person has 11 months their birthday may be in, and the third person has 10 months their birthday can be in. So we have:
For future reference, this forum is for introductions. Math queries should be posted in the appropriate forum. Your questions will be more likely to be answered there.