Now, there is also no known reason for the electron to have the mass and charge that we know it has. So, what is the probability of the electron having some specific mass? I seems it would be like asking what is the probability of randomly selecting some value on the real line, which, of course, is zero.
So, the probability of the mass of the electron, (assuming there is no theoretical basis for its given value -- and there seems to be none) is zero.
Now, you can extend that logic to every other value of all the fundamental constants we know. Lacking any theoretical basis for the values we have, the probability of these values is zero -- individually and collectively.