Prefix Probability in Stochastic Languages
According to their definition of PFA, to compute $Pr(w\Sigma^*)$ you simply need to compute the probability of having read $w$ after a random path of length $|w|$, which is easy.

Their model of PFA differs from the usual model: usually, for each state $q$ and letter $a$, we have $\sum_{q'} \delta(q,a,q')=1$, so you assume that in a run, the word is fixed beforehand and probabilities are played upon reading each letter.

Here, the setting is different: for each state $q$, we have $F(q)+\sum_{a,q'} \delta(q,a,q')=1$, meaning that a path is chosen at random (including the end), and induces a word. That is what makes the problem easier.