We investigate the confinement-deconfinement transition at finite temperature in terms of the probability distribution of Polyakov-loop complex-phase via the Jensen-Shannon divergence. The Jensen-Shannon divergence quantifies the difference of two probability distributions, namely the target and reference probability distributions. We adopt the complex-phase distributions of the spatially averaged Polyakov loop at $mu/T=0$ and $mu/T=ipi/3$ as the target and reference distributions, respectively. It is shown that the Jensen-Shannon divergence has the inflection point when the target system approaches the Roberge-Weiss endpoint temperature even in the finite-volume system. This means that we can detect the confinement-deconfinement transition from the structural change of probability distributions when we suitably set the reference probability distribution. It is also shown that we can pick up the information of the confinement-deconfinement transition from the quark number density by using the Fourier decomposition; Fourier coefficients have a long tail at around the transition temperature and show a divergent series in calculating the normalized kurtosis.
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