Cardy's annular crossing probability formula

Let $a=\log q$ for $q\in(0,1)$, and let $\mathbb{P}(N)(q)$ denote the probability of the annular crossing event $N$ described above. Set

$$\tau=-\frac{ia}{2\pi}.$$

Here $\eta$ denotes Dedekind's eta function. Cardy's conjectural formula. With these notations,

$$\mathbb{P}(N)=\sqrt{3}\frac{\eta(\tau)\eta(6\tau)^2}{\eta(3\tau)\eta(2\tau)^2}.$$

The formula was derived by Cardy using Coulomb-gas techniques in connection with conformal field theory, and is presented as the expected expression for the annular critical-percolation crossing probability. The source does not establish the formula here, so its resolution is left open in this record.