About 1 In 1000
Unless you have twins
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I believe the chances of having the same birthday as one of your parents is: 1 out of 183 and the chances of having the same birthday as both parents is: 1 out of 133,225
There is no simple answer since the times of conception may not be independent events.
Odds deal with sets of numbers. You haven't given a group to work with. For example, the odds of two people having the same birthday approaches certainty with a group of thirty or more, but finding someone with your birthday would require 180, just to give a fifty/fifty chance.
Believe it or not it happens very often for example three generations of women in my family have the same birthday i am the third generation I've seen it a lot more too so the odds are high. I agree, I am born on my mother's birthday and in school I had several friends who were also born on their mother's birthdays.
The fact that twins run in families is actually a myth. The odds of twins having twins is the same as a non-twin having twins. That is about 1 in 33.