Aharoni, Berger and Ziv recently proved the fractional relaxation of the
strong colouring conjecture. In this note we generalize their result as
follows. Let $k\geq 1$ and partition the vertices of a graph $G$ into sets
$V_1,\ldots, V_r$, such that for $1\leq i \leq r$ every vertex in $V_i$ has at
most $\max\{k, |V_i|-k \}$ neighbours outside $V_i$. Then there is a
probability distribution on the stable sets of $G$ such that a stable set drawn
from this distribution hits each vertex in $V_i$ with probability $1/|V_i|$,
for $1\leq i\leq r$.