  We consider the density at a point z = x + i y of critical percolation
clusters that touch the left [P_L(z)], right [P_R(z)], or both [P_{LR}(z)]
sides of a rectangular system, with open boundary conditions on the top and
bottom. The ratio C(z) = P_{LR}(z) / sqrt[P_L(z) P_R(z) Pi_h], where Pi_h is
the probability of horizontal crossing given by Cardy, is a universal function
of z and goes to a constant value C_0 = 2^(7/2) 3^(-3/4) pi^(5/2)
Gamma(1/3)^(-9/2) = 1.0299268... far from the ends. We observe numerically that
C(z) depends upon x but not y for wired b.c., and this result leads to an
explicit expression for C(z) via conformal field theory. For the semi-infinite
strip we also derive explict expressions for P_L(z), P_R(z), and P_{LR}(z), for
both wired and open b.c. Our results enable calculation of the finite-size
corrections to the factorization near an isolated anchor point, for the case of
clusters anchored at two boundary points. Finally, we present numerical results
for a rectangle with periodic b.c. in the horizontal direction, and find that
C(z) approaches a constant value C_1 = 1.022.
