  The mechanism of generation of the Bekenstein-Hawking entropy $S^{BH}$ of a
black hole in the Sakharov's induced gravity is proposed. It is suggested that
the "physical" degrees of freedom, which explain the entropy $S^{BH}$, form
only a finite subset of the standard Rindler-like modes defined outside the
black hole horizon. The entropy $S_R$ of the Rindler modes, or entanglement
entropy, is always ultraviolet divergent, while the entropy of the "physical"
modes is finite and it coincides in the induced gravity with $S^{BH}$. The two
entropies $S^{BH}$ and $S_R$ differ by a surface integral Q interpreted as a
Noether charge of non-minimally coupled scalar constituents of the model. We
demonstrate that energy E and Hamiltonian H of the fields localized in a part
of space-time, restricted by the Killing horizon $\Sigma$, differ by the
quantity $T_H Q$, where $T_H$ is the temperature of a black hole. The first law
of the black hole thermodynamics enables one to relate the probability
distribution of fluctuations of the black hole mass, caused by the quantum
fluctuations of the fields, to the probability distribution of "physical" modes
over energy E. The latter turns out to be different from the distribution of
the Rindler modes. We show that the probability distribution of the "physical"
degrees of freedom has a sharp peak at E=0 with the width proportional to the
Planck mass. The logarithm of number of "physical" states at the peak coincides
exactly with the black hole entropy $S^{BH}$. It enables us to argue that the
energy distribution of the "physical" modes and distribution of the black hole
mass are equivalent in the induced gravity. Finally it is shown that the
Noether charge Q is related to the entropy of the low frequency modes
propagating in the vicinity of the bifurcation surface $\Sigma$ of the horizon.
