The numbers where all three digits are same are: 000,111,222,333,444,555,666,777,888,999.
So what is the probability?!
I realize that those are all the numbers where the three digits are the same, 10/999? There are only 10 numbers where all three digits are the same, but there are 999 unique numbers (000, 001, 002...997, 998, 999, etc).