  We consider random holomorphic dynamical systems on the Riemann sphere whose
choices of maps are related to Markov chains. Our motivation is to generalize
the facts which hold in i.i.d. random holomorphic dynamical systems. In
particular, we focus on the function $T$ which represents the probability of
tending to infinity. We show some sufficient conditions which make $T$
continuous on the whole space and we characterize the Julia sets in terms of
the function $T$ under certain assumptions.
