Q:

How do I mathematically express this?

Probability of getting selected  from a pool of 5 applicants but the available slots are 10 (more than the applicants).
I know that it should not go beyond 100%, how do I do this?
Im just coming from the fact that let's say 2 applicants and 6 slots, therefore 33% of getting "chosen."

A:

If I understand correctly, you ask what is the probability that a candidate out of 5 is chosen when you choose all 5, since you have plenty of available slots.
An intuitive way of defining the probability of an event is the ratio between the number of favourable cases and the number of possible cases. For instance, if you had 3 applicants and 1 slot, then you would have 1 favourable case and three possible ones, and the probability would be $\frac{1}{3}$. 
In your situation, all the possible cases are favourable, therefore the probability of getting selected is $1$.

