Some consequences of SLE and Conformal Invariance are tested in the 2d random-bond Potts model by means of Monte Carlo simulations. We consider domain walls between different spin states induced in the system by symmetry-breaking boundary conditions. Conformal Invariance required by SLE is known to hold for this system. For instance, magnetization profiles and correlation functions in confined geometries have allowed in the past for accurate estimations of critical exponents and numerical computation of the central charge for a localisation of the random fixed point. We show that the probability of passage of the interface at the left of a given point is well reproduced by the Schramm formula and leads to a SLE parameter kappa compatible with that extracted from the fractal dimension of the interface.