Question

why is it possible to create kaons by colliding protons?

Answer 1

All collections of particles with the total energy and momentum equal to the initial one, total B=2, total electric charge Q=2, total lepton charge L=0, and total spin conserved (or at least integer-valued) occur as final states of the proton-proton collisions with a nonzero probability.

If one includes extremely unlikely processes linked to grand unification etc., even the conditions about the conservation of B,L may be relaxed.Of course, this is just a very qualitative, nearly vacuous statement: everything that isn't banned (by conservation laws i.e. by symmetries) will happen with a nonzero probability. In reality, it matters what the probabilities are. Some of them are vastly greater than others. In most collisions, one only creates the same protons, a couple of pions, maybe kaons, photons, sometimes antiprotons, muons – directly or from decays of mesons. Only rarely, one produces heavy particles such as Z-bosons and W-bosons. Even more rarely, one produces Higgs bosons etc. Only hundreds of Higgs bosons have been produced in the 400 trillion collisions (per detector) at the LHC. The number of Z-bosons (or top quarks) is much higher but still a tiny fraction of those 400 trillion collisions.

It's meaningless to give a longer answer to this question because it implicitly contains all of experimental particle physics. One is interested not only about the "types" of particles in the final state but also about their energies and directions of motion (including the relative ones). Quantum field theory calculates all these probabilities (or cross sections); in some sense, it doesn't calculate anything else. So a full answer to this question also includes the explanation of all things that may be calculated from quantum field theory – all of particle physics.