Because each number is equally as likely as every other number. If you know you're more likely to get certain numbers, or in this case have no chance of getting certain other numbers, it is by definition _less random_.
No, that has nothing to do with randomness. It is however a different distribution than expected.
Think about the odds of a uranium atom decaying in a given second. Certainly a random event, yet for most seconds, the value is False, not True.
Ah. My reasoning, with the normal distribution, was that zero was at the left most end of the curve and with a pretty much non-existent chance of appearing.