The space-time prism is a key concept in time geography that captures both spatial and temporal constraints on an object's potential mobility. For mobility within transportation networks, network-time prisms (NTPs) delimit accessible locations with respect to time given scheduling constraints, movement constraints, and speed limits imposed by the network. The boundary of a NTP has been used as a measure of individuals' accessibility within a network. However, the interior structure has lacked quantitative characterization, including the distribution of visit probabilities at accessible locations. This article models visit probabilities within NTPs using two types of Markov techniques: (1) Brownian motion on undirected graphs for nonvehicular mobility (e.g., walking) and (2) continuous-time semi-Markov process for vehicular mobility (e.g., biking, driving). Based on these methods, we simulate nonvehicular and vehicular visit probabilities and visualize these distributions. For vehicular mobility, we compare the simulated visit probabilities with empirical probabilities derived from trajectories collected by Global Positioning System (GPS) in New York City, USA. The visit probabilities provide a quantitative description of individuals' potential mobility within a NTP and a foundation for developing the refined accessibility benefit and cost measures that go beyond the binary nature of classical NTPs.