This paper presents a modified channel likelihood model for optical communication systems with a photon-counting array receiver where photon-counting events are impaired by undesirable dead time and jitters. After the photon-counting detector detects a photon, the detector will go into a period of dead time under which it cannot detect any incident photons. In this context, the channel will have memory. We derive the channel likelihood in the presence of the detector dead time and the random jitter of the photon arrival. The impact of dead time and jitters on the performance of a pulse-position-modulated (PPM) optical communication system is also investigated. The simulation results indicate that the modified channel likelihood expressions can obtain a more obvious performance gain under the context of a stronger background noise, fewer detection elements, longer dead time and bigger jitter.