Answer:
Person A can be born on any day of the year since they’re the first person we’re asking. The probability of being born any day of the year is 1 or more specifically: 365/365.
Since Person B must be born on the same day as Person A their probability is 1/365.
We want both of these events to happen so multiply the probabilities:
365
So you have a 0.27% chance of walking up to a stranger and discovering that their birthday is the same day as yours.
I think you are happy with this answer