A friend and I had debate what the probability of being born on Feb 29 is?

1)I said it is Probability of Leap yearandFeb 29 which is $\displaystyle \frac{1}{4}\frac{1}{366}=\frac{1}{1464}$

2)He said in 4 full years there are 1461 days thus the probability is $\displaystyle \frac{1}{1461}$

Who is correct? Both explainations are reasonable.

I am thinking that the probability of a year being leap is notexactly$\displaystyle 1/4$ but close to it. Which is why he and I have a minor discrepancy.