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 e^{i x} to 1 the probability of the event that γ avoids the disk of radius q centered at zero decays like exp (- b π x / (1 - q)) if either b ∈ [5 / 8, 1] ∪ [5 / 4, ∞) and x ∈ (0, π], or if b ∈ (1, 5 / 4), x ∈ (0, π), and b x ≤ π.