Step 1 :There are 365 days in a year (ignoring leap years). If Mike is guessing randomly, then there is only 1 day that is Kelly's birthday.
Step 2 :Therefore, the probability that Mike will guess correctly is 1 out of 365.
Step 3 :Final Answer: The probability that Mike will guess Kelly's birthday correctly is \(\boxed{\frac{1}{365}}\).