The birthday paradox with a twist

1/98345365761254

Using this approximating formula from the Birthday Problem at wikipedia
p(n,d) = 1-exp(-n(n-1)/2d)
with n=10000 and d=366*26^3 and assuming that all days/initials are equally probable, the probability of a match is approximately 0.999578575.

Given that families share a last initial and kids are often named after parents, the probability is likely higher.