  The decay $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ is studied
in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV
using data corresponding to an integrated luminosity of 5 $\mathrm{fb}^{-1}$
collected by the LHCb experiment. In the $\Lambda_{c}^+ K^{-}$ system, the
$\Xi_{c}(2930)^{0}$ state observed at the BaBar and Belle experiments is
resolved into two narrower states, $\Xi_{c}(2923)^{0}$ and $\Xi_{c}(2939)^{0}$,
whose masses and widths are measured to be $$ m(\Xi_{c}(2923)^{0}) = 2924.5 \pm
0.4 \pm 1.1 \,\mathrm{MeV}, \\ m(\Xi_{c}(2939)^{0}) = 2938.5 \pm 0.9 \pm 2.3
\,\mathrm{MeV}, \\ \Gamma(\Xi_{c}(2923)^{0}) = \phantom{000}4.8 \pm 0.9 \pm 1.5
\,\mathrm{MeV},\\ \Gamma(\Xi_{c}(2939)^{0}) = \phantom{00}11.0 \pm 1.9 \pm 7.5
\,\mathrm{MeV}, $$ where the first uncertainties are statistical and the second
systematic. The results are consistent with a previous LHCb measurement using a
prompt $\Lambda_{c}^{+} K^{-}$ sample. Evidence of a new $\Xi_{c}(2880)^{0}$
state is found with a local significance of $3.8\,\sigma$, whose mass and width
are measured to be $2881.8 \pm 3.1 \pm 8.5\,\mathrm{MeV}$ and $12.4 \pm 5.3 \pm
5.8 \,\mathrm{MeV}$, respectively. In addition, evidence of a new decay mode
$\Xi_{c}(2790)^{0} \to \Lambda_{c}^{+} K^{-}$ is found with a significance of
$3.7\,\sigma$. The relative branching fraction of $B^{-} \to \Lambda_{c}^{+}
\bar{\Lambda}_{c}^{-} K^{-}$ with respect to the $B^{-} \to D^{+} D^{-} K^{-}$
decay is measured to be $2.36 \pm 0.11 \pm 0.22 \pm 0.25$, where the first
uncertainty is statistical, the second systematic and the third originates from
the branching fractions of charm hadron decays.
