This is actually an open question.
So far what we are able to state from theoretical considerations are restrictions in terms of the conservation laws that we have observed. These tells you for example that the whole momentum in a reaction is conserved, an the mass-energy, or some quantum numbers. And this already constraints much of what can come out from certain reaction: for example a photon interacting with charged matter can originate a positron-electron pair, and while you cannot say how probable is this without measuring experimentally, you can already say that measuring the probability for electrons you will have the one for positrons because they only can come in pair and due to charge and momentum conservation.
But when it comes to predicting ratios of outgoing particles, theoretically this would need as well the full knowledge of the coupling constants among all particles, or in other words, the exact form of the interactions, and this cannot be provided so far without experimental values.
We are more or less able to state the form of our fundamental Lagrangian, writing terms for all kinds of interactions, but we are unable to give values to the constants without experimental evidence.
So what we do so far is: we elaborate constraints from theory based on our current understanding, this helps processing the experimental information and deducing unknown yields based on the known ones, and find relative yields between particles which gives these probabilities.