  The decay process $\Xi_{b}^{-} \rightarrow pK^{-}K^{-}$ is studied with the
final state interaction approach by considering the contributions from the
$S$-wave meson-baryon interactions, and also the intermediate state
$\Lambda(1520)$ in the $D$-wave. The low-lying resonances $\Lambda(1405)$ and
$\Lambda(1670)$ have significant contributions, which are both dynamically
generated from the $S$-wave final state interactions with isospin $I=0$.
Furthermore, the $\Lambda(1520)$ state also has important contributions from
$D$-wave. With these resonances contributions, the experimental data of the
lower $pK^{-}$ invariant mass distributions are well described. We also discuss
the contribution of another resonance in the $S$-wave with isospoin $I=1$,
which cannot be ignored. Moreover, some of the branching fractions obtained for
the corresponding decay channels are consistent with the experimental
measurements.
