For a radiative transition, these three mechanisms are always present at the same time. To make a laser medium, conditions have to be found that favour stimulated emission over absorption and spontaneous emission. Thus, both the right medium and the right conditions must be chosen to produce the laser effect.
An incident photon of energy has an equal chance of being absorbed by a ground-state atom as being duplicated (or amplified!) by interacting with an excited-state atom. Absorption and stimulated emission are really two reciprocal processes subject to the same probability. To favour stimulated emission over absorption, there need to be more excited-state atoms than ground-state atoms.
Spontaneous emission naturally tends to empty the upper level so this level has to be emptied faster by stimulated emission. It has been proved that stimulated emission is much more likely to happen if the medium used is flooded with light (i.e. with a large number of photons). A good way to do this is to confine the photons in an optical cavity.