The answer depends on where in the world you are. In some places, where hospital [or maternity unit] births are more popular, the medical staff prefer to deliver babies during weekdays so that they can have time with their own families at weekends. As a result, the distribution of births is not uniform across days of the week.
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The probability of two people's birthday being the same is actually more likely than many would think. The key thing is to note that it doesn't matter what the first person's birthday is. All we need to work out is the probability that the second person has a birthday on any specific day. This probability is 1/365.25 The probability that they were born on June 10th is 1/365.25. The probability that they were born on February 2nd is 1/365.25 and the probability that they were born on the same day as you is 1/365.25
The probability, over presidents of all organisations, through all of time, is 1.
The probability that two persons share the same birth date can be calculated using the concept of the birthday paradox. In a group of 23 people, there is a probability of approximately 50% that two individuals share the same birth date. This probability increases as the number of people in the group increases due to the increasing number of possible pairs to compare. The calculation involves considering the complementary probability of no one sharing a birthday and subtracting it from 1 to find the probability of at least one shared birthday.
Birthdays are not uniformly distributed over the year. Also, if you were born on 29 February, for example, the probability would be much smaller. Ignoring these two factors, the probability is 0.0082
1/7