Restricting SLE(8/3) to an annulus

We study the probability that chordal ${\text{SLE}}_{8\mathrm{/}3}$ in the unit disk from $\exp (ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find the initial/boundary-value problem satisfied by this probability as a function of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one this probability decays like $\exp (-cx\mathrm{/}(1-q))$ with $c=5\pi \mathrm{/}8$ for $x\in [0,\pi ]$. We also give a representation of this probability as a functional of a Legendre process.