Cardy's formula in Carleson's version for critical percolation

Let $D$ be a simply connected domain in the complex plane, and let $a,b,c,x$ be boundary points in counterclockwise order. Suppose that $D$ is conformally equivalent to the equilateral triangle $ABC$, with $a,b,c$ mapped respectively to $A,B,C$ and $x$ mapped to $X\in[CA]$. Consider critical percolation on lattice approximations of $D$, with mesh tending to zero. Cardy's formula, Carleson's version. In the scaling limit, the probability of an open crossing in $D$ from the boundary part $(ab)$ to the boundary part $(cx)$ is

$$\frac{CX}{CA}.$$

This is the conformally invariant crossing-probability formula predicted by Cardy and reformulated geometrically by Carleson. Smirnov's theorem establishes this formula for critical site percolation on the triangular lattice; the source presents the statement in the context of the resulting conformal invariance.