Because is not a number is not defined and therefore equals no number.

It is simply not defined.

Now it is true that if we randomly pick any number in the probably of that number being is zero.

That does not mean that cannot be picked. It can with probability zero.

This is a proper question.

Suppose we randomly pick any number in , what is the probability that the number is within 0.2 units of ?

Well the answer is because we asking .

Does that make sense to you?