  We call a \emph{comb} a map $f:I\to [0,\infty)$, where $I$ is a compact
interval, such that $\{f\ge \varepsilon\}$ is finite for any $\varepsilon$. A
comb induces a (pseudo)-distance $\dtf$ on $\{f=0\}$ defined by $\dtf(s,t) =
\max_{(s\wedge t, s\vee t)} f$. We describe the completion $\bar I$ of
$\{f=0\}$ for this metric, which is a compact ultrametric space called
\emph{comb metric space}.
  Conversely, we prove that any compact, ultrametric space $(U,d)$ without
isolated points is isometric to a comb metric space. We show various examples
of the comb representation of well-known ultrametric spaces: the Kingman
coalescent, infinite sequences of a finite alphabet, the $p$-adic field and
spheres of locally compact real trees. In particular, for a rooted, locally
compact real tree defined from its contour process $h$, the comb isometric to
the sphere of radius $T$ centered at the root can be extracted from $h$ as the
depths of its excursions away from $T$.
