Across North America, decades of fire suppression and recent patterns of human settlement have combined to increase the risks that wildland fires pose to human life, property, and natural resource values. Various methods can be used to reduce fuel hazards and mitigate these risks, but funding and other constraints require that these fuel treatments be prioritized across large landscapes. An understanding of where fire is most likely to occur on the landscape would allow managers to strategically prioritize their fuel hazard reduction efforts and to design effective fire management plans. Predictive models of the probability of burning can be developed using empirical relationships between landscape variables and historic fire data, but this approach is limited to areas with extensive records of historical fires. Furthermore, models that are empirically derived from landscape variables have low predictability because fire spread is a spatially contagious process; the probability of any location burning depends primarily on whether neighboring locations are likely to burn. This spatial context of fire occurrence can be addressed with a more mechanistic modeling approach. In this paper, I present a modeling approach whereby a map of the probability of burning is derived using information on the spatial distribution of fuels, topography, and ignitions. This approach uses generally available spatial data, climate information, standard geographic information system functions, and equations that describe the physics of fire spread. The potential use and application of the approach are discussed, and its performance is evaluated via a qualitative comparison with 20th-century fire occurrence data from the Selway-Bitterroot Wilderness in northern Idaho and western Montana.