That's not a uniform distribution. Probability doesn't remember previous state, so the chance of picking the number 241 out of 1 million numbers remains exactly

That's not a uniform distribution. Probability doesn't remember previous state, so the chance of picking the number 241 out of 1 million numbers remains exactly the same after picking 241 once. In particular, the chance of getting no duplicate numbers if you pick a million times, is very close to zero.