A quantity of interesting in Percolation theory is the distribution of sizes for the small clusters in percolation models.

This can be quantified by the total number of clusters of size $s$, $n_s$. Sometimes one works with $n_s/N$ instead, to eliminate the scaling with $N$ that would make $n_s \rightarrow \infty$ as $N \rightarrow \infty$.

One can also work with the probability that a random node belongs to a cluster of size $s$, which can be easily seen to be $\pi_s = \frac{s n_s}{N} = \frac{\#\text{ of nodes in clusters of size }s}{\text{total }\#\text{ of nodes}}$. This is clearly the probability of picking a node inside a cluster of size $s$ given a particular network configuration. In the case of Percolation on random graphs and networks, it's also the probability that a random network configuration (following the appropriate probability distribution defining the network ensemble) makes a particular chosen node be in a cluster of size $s$. This is because the two operations are statistically independent.

$\pi_s$ can be shown to decrease exponentially with s in the subcritical regime, and it decays more slowly in the supercritical regime. (see here). At the critical point, the cluster size follows a power law distribution (as do for instance avalanche sizes in the sandpile model at criticality).