Probability: proportion of 1000 random lists for x that contain the same nrs

I want to estimate, for groups of x persons, the probability that at least two of them have the same birthday. I want to repeat this process 1000 times. So I'm looking for the number of 1000 random birthday lists that contain the same birthday. (in other words, I need the probability)

Let' say a function which calculates a random birthdays is ($x$ can be from $x=1$ to $x=365$)

birthdays[x_] := RandomInteger[{1, 365}, x]

is my answer. Take x=25 and determine whether birthdays[x] contain equal numbers.

bday1 = birthdays[25]

Length[bday1]

ubday1 = Union[bday1]

Length[ubday1] is my answer.

This is my answer so far; and I don't know whether its correct or not.

birthprob[x_] := Count[Table[RandomInteger[{1, 365}, x], {1000}], 

Could someone help me?