  We have numerically studied the properties of the interface induced in the
ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary
conditions. The fractal dimension $d_f$ of the interface was determined. The
corresponding SLE parameter $\kappa$ was estimated to be $\kappa\simeq
3.18(6)$, compatible with previous estimate. On the other hand, we estimated
$\kappa$ independently from the probability of passage of the interface at the
left of a given point. The numerical data are well reproduced by the Schramm
theoretical prediction and the fit leads to $\kappa\simeq 3.245(10)$, in
agreement with the first estimate. This provides evidences that the geometric
properties of spin interfaces in the random 3-state Potts model may be
described by chordal ${\rm SLE}_\kappa$.
