  The probability distribution of the net baryon number is investigated within
the functional renormalization group approach. We find that the Roberge-Weiss
periodicity related to the Z(3) symmetry of the gluon fields results directly
in that, states of the net baryon number $N_B=N\pm 1/3$ with $N\in\mathbb{Z}$
are prohibited, and only those of $N_B=N$ are possible. By employing the
probability distribution of the net baryon number, we also compute the
cumulants of the baryon number distribution, which are found to be well
consistent with those obtained from the generalized susceptibilities. A
question about the relation between the color confinement and the probability
distribution of net baryon number is put forward.
