  In the near future, the neutrinoless double-beta ($0\nu\beta\beta$) decay
experiments will hopefully reach the sensitivity of a few ${\rm meV}$ to the
effective neutrino mass $|m^{}_{\beta\beta}|$. In this paper, we tentatively
examine the sensitivity of future $0\nu\beta\beta$-decay experiments to
neutrino masses and Majorana CP phases by following the Bayesian statistical
approach. Provided experimental setups corresponding to the sensitivity of
$|m^{}_{\beta\beta}| \simeq 1~{\rm meV}$, the null observation of
$0\nu\beta\beta$ decays in the case of normal neutrino mass ordering leads to a
very competitive bound on the lightest neutrino mass $m^{}_1$. Namely, the
$95\%$ credible interval turns out to be $1.6~{\rm meV} \lesssim m^{}_1
\lesssim 7.3~{\rm meV}$ or $0.3~{\rm meV} \lesssim m^{}_1 \lesssim 5.6~{\rm
meV}$ when the uniform prior on $m^{}_1/{\rm eV}$ or on
$\log^{}_{10}(m^{}_1/{\rm eV})$ is adopted. Moreover, one of two Majorana CP
phases is strictly constrained, i.e., $140^\circ \lesssim \rho \lesssim
220^\circ$ for both priors of $m^{}_1$. In contrast, if a relatively worse
sensitivity of $|m^{}_{\beta\beta}| \simeq 10~{\rm meV}$ is assumed, the
constraint becomes accordingly $0.6~{\rm meV} \lesssim m^{}_1 \lesssim 26~{\rm
meV}$ or $0 \lesssim m^{}_1 \lesssim 6.1~{\rm meV}$, while two Majorana CP
phases will be essentially unconstrained. In the same statistical framework,
the prospects for the determination of neutrino mass ordering and the
discrimination between Majorana and Dirac nature of massive neutrinos in the
$0\nu\beta\beta$-decay experiments are also discussed. Given the experimental
sensitivity of $|m^{}_{\beta\beta}| \simeq 10~{\rm meV}$ (or $1~{\rm meV}$),
the strength of evidence to exclude the Majorana nature under the null
observation of $0\nu\beta\beta$ decays is found to be inconclusive (or strong),
no matter which of two priors on $m^{}_1$ is taken.
