I am confused about the concept of uniform distribution and random number. Does random number follow uniform distribution or does random number not follow any distribution?
Traditionally, random is just that, random. There is nothing that guarantees that after 100 random numbers, at least one of them is non-zero. You'd probably think something is broken, and while you'd probably be right, it is just as possible as any other combination of numbers in the same given range.
Uniform distribution will ensure that statistically speaking, your values will be spread out across a given range. In that case if you got 100 random uniformly distributed numbers and they were all zero, something is definitely broken.