  We present the first measurements of absolute branching fractions of
$\Xi_c^0$ decays into $\Xi^- \pi^+$, $\Lambda K^- \pi^+$, and $p K^- K^- \pi^+$
final states. The measurements are made using a data set comprising $(772\pm
11)\times 10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance
with the Belle detector at the KEKB $e^+e^-$ collider. We first measure the
absolute branching fraction for $B^- \to \bar{\Lambda}_c^- \Xi_c^0$ using a
missing-mass technique; the result is ${\cal B}(B^- \to \bar{\Lambda}_c^-
\Xi_c^0) = (9.51 \pm 2.10 \pm 0.88) \times 10^{-4}$. We subsequently measure
the product branching fractions ${\cal B}(B^- \to \bar{\Lambda}_c^-
\Xi_c^0){\cal B}(\Xi_c^0 \to \Xi^- \pi^+)$, ${\cal B}( B^- \to
\bar{\Lambda}_c^- \Xi_c^0) {\cal B}(\Xi_c^0 \to \Lambda K^- \pi^+)$, and ${\cal
B}( B^- \to \bar{\Lambda}_c^- \Xi_c^0) {\cal B}(\Xi_c^0 \to p K^- K^- \pi^+)$
with improved precision. Dividing these product branching fractions by the
result for $B^- \to \bar{\Lambda}_c^- \Xi_c^0$ yields the following branching
fractions: ${\cal B}(\Xi_c^0 \to \Xi^- \pi^+)= (1.80 \pm 0.50 \pm 0.14)\%$,
${\cal B}(\Xi_c^0 \to \Lambda K^- \pi^+)=(1.17 \pm 0.37 \pm 0.09)\%$, and
${\cal B}(\Xi_c^0 \to p K^- K^- \pi^+)=(0.58 \pm 0.23 \pm 0.05)\%.$ For the
above branching fractions, the first uncertainties are statistical and the
second are systematic. Our result for ${\cal B}(\Xi_c^0 \to \Xi^- \pi^+)$ can
be combined with $\Xi_c^0$ branching fractions measured relative to $\Xi_c^0
\to \Xi^- \pi^+$ to yield other absolute $\Xi_c^0$ branching fractions.
