Modeling a set of probabilistic concurrent processes
One approach is to model it as a composition of $N+1$ processes: a scheduler process, plus your $N$ basic processes.  At each time step, the scheduler process selects which basic process will execute next.  Your scheduler could be randomized: for instance, at each time step, it could choose which basic process to execute next uniformly at random, if you wanted.

Now the transitions of the entire system, and their probabilities, should be easy to derive.  A state of the system is of the form $\langle s_0,s_1,\dots,s_N \rangle$ where $s_0$ is the state of the scheduler and $s_i$ is the state of the $i$th basic process.  Each transition might have the form $\langle s_0,\dots,s_N \rangle \to \langle s'_0,s_1,\dots,s_{i-1},s'_i,s_{i+1},\dots,s_N \rangle$ (where $i$ is a deterministic function of $s_0$, and with probability given by the probability of $s_0 \to s'_0$ in the scheduler multiplied by the probability of $s_i \to s'_i$ in the $i$th basic process).

There are probably other ways to model it as well, maybe better ones for all I know.  This is just one possibility that occurs to me.