  We give an example of an Ahlfors $3$-regular, linearly locally connected
metric space homeomorphic to $\mathbb{R}^3$ containing a nondegenerate
continuum $E$ with zero capacity, in the sense that the conformal modulus of
the set of nontrivial curves intersecting $E$ is zero. We discuss this example
in relation to the quasiconformal uniformization problem for metric spaces.
