The probability of getting a 0 is the same for every digit. However, in my opinion, the probability of getting a number that starts with two zeros is 1/10 * 1/10, and the probability of getting a number that starts with the same two digits is 10 * 1/10 * 1/10.

But the probability to receive one number or the other are the same.

By random chance you probably wouldn't get that many zeros. Of course, one could say it's just as random as any other string, but..