  We study visibility inside the vacant set of three models in $\mathbb R^d$
with slow decay of spatial correlations: Brownian interlacements, Poisson
cylinders and Boolean model. For each of them, we obtain sharp asymptotic
bounds on the probability of visibility to distance $r$ in some direction in
terms of the probability of visibility to distance $r$ in a given direction. In
dimensions $d\geq 4$, the ratio of the two probabilities has the same scaling
$r^{2(d-1)}$ for all three models, but in lower dimensions the scalings are
different. In particular, we improve some main results from arXiv:0905.4874 and
arXiv:1709.09052.
