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 .