stimulated emission reason
Consider the electron at an excited energy level (two level model; ground state and excited state). It has nowhere to go but to come down to the ground level. The way it comes down to ground state is by spontaneous emission. The result is electron in the ground state and the photon released. This is a random process (just like a radioactive decay) and we can ascribe a half-life for this spontaneous emission.
The electron in the excited state cannot absorb another photon (there is no corresponding energy level available). However, another photon in the close vicinity of the excited electron can interact and cause the excited electron to come to the ground state and release the photon (in addition to the stimulating one).
You have asked "why" and the reason for the stimulation effect is part of quantum mechanics. In simple terms, photons are bosons and the state in which there are more photons are more stable and the interaction between the photon and the excited electron is electrostatic in nature and the two resulting photons are in same polarization and same phase.
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