Why the probability is $0$ but possible We want to take a random number from natural numbers how much is the probability that,the number be $1$?
When we want to say the probability we say it is $0$ but we say zero for impossible things but that is possible.I know that every number divided by infinity is zero but maybe we take $1$ what about that?
 A: There are two issues here:
Firstly, you haven't specified what probability distribution on the natural numbers we should assume. You probably mean one which is in some sense uniform: $Pr(0)=Pr(1)=Pr(2)=\cdots$ to infinity. However there is no such distribution, as explained here.
The other issue is that "possible" isn't a very well-defined mathematical term. When we talk about probability formally, we usually talk about a space of outcomes $X$ (eg. in this case that would be the natural numbers) and a probability measure $P$ which takes subsets of $X$ and gives the probability of the outcome being in that subset (there's also something else called a $\sigma$-algebra but there's no need to add that extra confusion here). Probabilists then do not distinguish between probability measures that differ on sets of zero probability events. For example, the $P$ which uniformly picks a number in the interval $[0,1]$ and the $P'$ which uniformly picks a number in $[0,1]\setminus\{0.42\}$ are considered the same distribution since in either case the outcome has a zero probability of being in the set $A=\{0.42\}$. However, in the first case you would say $A$ is "possible," in the second case you would not.
