  We investigate the physics reach and potential for the study of various
decays involving a $b \to s \nu \bar{\nu}$ transition at the Future Circular
Collider running electron-positron collisions at the $Z$-pole (FCC-ee). Signal
and background candidates, which involve inclusive $Z$ contributions from
$b\bar{b}$, $c\bar{c}$ and $uds$ final states, are simulated for a proposed
multi-purpose detector. Signal candidates are selected using two Boosted
Decision Tree algorithms. We determine expected relative sensitivities of
$0.53\%$, $1.20\%$, $3.37\%$ and $9.86\%$ for the branching fractions of the
$B^{0} \to K^{*0} \nu \bar{\nu}$, $B^{0}_{s} \to \phi \nu \bar{\nu}$, $B^{0}
\to K^{0}_{S} \nu \bar{\nu}$ and $\Lambda_{b}^{0} \to \Lambda^{0} \nu
\bar{\nu}$ decays, respectively. In addition, we investigate the impact of
detector design choices related to particle-identification and vertex
resolution. The phenomenological impact of such measurements on the extraction
of Standard Model and new physics parameters is also studied.
