In energy/momentum space the solutions of the wavefunctions give specific energy levels, with a width due to quantum mechanical uncertainties due to higher order exchanges.Because of energy and momentum conservation, there is no "probable energy" for a given electron (except within the width). There are no independent conservation laws in space-time. The energy momentum conservation laws (energy momentum) constrain the space location ,orbitals, of electrons around the atoms and molecules to be in a "probable location".
See the possible orbitals of an electron around an atom.
If the electron is in a 2p state, i.e.higher than ground energy, there is a probable hole in the 1s state. In space time it means that part of the time there is no electron where there would have been if the electron were in the ground state.
Extending this to a solid is not easy , the way the band structure model fits the solid state data, because again energy and momentum conservation affect the space-time probability loci in a probability fuzzy way, but this does not mean that the concept of a "hole" is not correct. It is a probable hole in a complicated quantum mechanical orbitals solution for the solid. There is no contradiction with the band theory, imo.
To answer the title :
If an electron-hole pair is formed, where does the electron “go”?
To an appropriate to its energy level orbital of the solid, with the probability given by the solution of the space-time wavefunction of the solid.