the probability of guessing a number Choose any natural number.

For example I would choose:

3852011231231280130218920382342312420234801232321241231212131234 (and so for for another few bilions of digits)

What's the probability that somebody can guess it ? 

Since there are infinite natural numbers I saw that the answer is 0.
(this is from a book from gregory chaitin)

is that correct ? 

or is it more correct to say that it's very very very.... unlikely but still possible.
To be able to answer your question, you'd have to specify how someone would guess an arbitrary natural number. Since $\mathbb{N}$ is coutable infinite, there's no such thing as a uniform probability distribution over $\mathbb{N}$. Such a distribution would have to assign the same probability to each natural number (to be uniform), but that'd make the sum of all probabilities $+\infty$, not $1$ as you'd want for a probability distribution.

There are non-uniform distributions over $\mathbb{N}$ though, but to compute what the probability of 3852011231231280130218920382342312420234801232321241231212131234 under such a distribution would be, you first have to decide which distribution to use.
You are correct. The answer is zero.