What is the probability of having children with the same birth date (born in different years)?

In the real world, this problem is going to be quite complex because it needs to take into consideration various factors and settings, such as the difference on the degree of intimacy between the parents on various days of the year, holidays, work schedule, activities and many other things.

However, if we disregard any other extra factors and assume that the degree of intimacy between parents is the same every day of the year, then the probability of these parents having children with the same birth date is 1 out of 365 days in a regular year and 1 out of 366 during leap years.