A representation in the form of the Faddeev-Popov path integral is constructed for solving the equations of quantum geometrodynamics (QGD). It is shown that QGD is equivalent to canonical quantization of gravity in a unitary gauge. Given the state of the gravitational field on the initial Cauchy hypersurface, a wave function of closed universe is constructed so that it satisfies the QGD equations. Using the principles of canonical quantization, a probabilistic interpretation of this wave function is constructed in a fashion close to Everett's concepts of quantum mechanics.