Given a distribution over graphs with $n$ nodes having the "scale-free" property, I would like to compute for a pair of vertices $(a,b)$ the probability that they are connected (or more precisely the probability that there is a directed edge from $a$ to $b$).

Is it possible to have such probability distribution ?

Note that the case without the "scale-free" property is not a problem. I can define the probability of having an edge from $a$ to $b$ as $P((a,b))=1/2$ for all $a, b$, $a \neq b$ in the graph.

Thank you.