Starting from a simple observation relating the Brownian loop soup and SLE loop measure, and exploiting the connections between the Brownian loop soup, Liouville quantum gravity, and Liouville conformal field theory, we derive the joint law of the outer and inner boundaries of a Brownian loop-soup cluster with respect to a given point. In particular, we compute the probability that the two boundaries do not touch. We also extend this result to a single Brownian loop by taking the zero-intensity limit of the loop soup. This is based on a joint work with Gefei Cai, Jiaqi Liu, Xin Sun and Baojun Wu.