“Not knowing the exact math doesn’t imply that you can´t establish that the probability of something is low”
Please acknowledge that this particular statement is true, after you do that I will deal with the other 100 objections that you might have
While that is true in general, it does require some knowledge of the correlations between different events. Without such, even a ball park figure on the end probability is impossible.
For example, suppose that you ask for a string of 50 symbols, each with 90 possibilities. Assuming independence, the end probability of a correct match would be one in 90^50, which is vanishingly small.
If you did such a random selection 50,000 times, the end probability of getting a match would still be vanishingly small.
But, suppose instead that you randomly select a string then produce 100 children by randomly selecting a symbol and randomly changing it. Then you pick the child that is closest to the target string. Let that child produce 100 randomly generated children in the same way.
Now, ask yourself what the probability of getting a match for the target string is after 500 generations (still 50,000 trials, notice).
The end probability now is almost 1.
So, no, you cannot even estimate the probability accurately unless you have the correct formulation (or something quite close to it). You cannot even know if the probability is small if you calculate it in the wrong way.