  SLE($\kappa,\rho$) is a variant of the Schramm-Loewner Evolution which
describes the curves which are not conformal invariant, but are self-similar
due to the presence of some other preferred points on the boundary. In this
paper we study the left passage probability (LPP) for SLE($\kappa,\rho$)
through field theoretical framework and find the differential equation which
govern this probability. This equation is solved (up to two undetermined
constants) for the special case $\kappa= 2$ and $h_\rho = 0$ for large x0 at
which the boundary condition changes. This case may be referred to the Abelian
sandpile model with a sink on the boundary. As an example, we apply this
formalism to SLE($\kappa,\kappa-6$) which governs the curves that start from
and end on the real axis.
