Quantum dynamics of the states of three resonantly interacting two-level fluorescent particles is considered. It is shown that resonant laser excitation may lead to state inversion and to entanglement of energy states of the particles. The exact analytical solution of the problem in the case of zero decoherence is given. It describes complex dynamics in the case of strong laser radiation as well as easier and more perspective for practical implementation case of weak laser field. For the latter situation, the approximate solution obtained by the perturbation theory application is also presented and tested against the exact theoretical solution and numerical simulation.