Asymptotic probabilities for conformal restriction measures for an annulus

We show that for the conformal restriction measure with exponent b in the unit disk on hulls γ connecting eix to 1 the probability of the event that γ avoids the disk of radius q centered at zero decays like exp(−bπx/(1−q)) if either b∈[5/8,1]∪[5/4,∞) and x∈(0,π], or if b∈(1,5/4), x∈(0,π), and bx⩽π.