The ambient probability of near mid-air collision (NMAC) is the probability of NMAC in a particular environment without any risk mitigation due to, for example, air traffic control (ATC) surveillance, separation assurance, or avoidance maneuvers. This probability has also been referred to as the baseline probability of NMAC, and is of particular interest when determining the required risk mitigation. In past literature, this probability has been calculated based on estimates of aircraft density, assumptions of locally uniformly distributed aircraft, and the use of gas models for making these calculations. Stakeholders for unmanned aircraft operations have become increasingly interested in determining such probabilities within specific airspace volumes to identify suitable locations and times of operation for flight of unmanned aircraft in non-restricted civil airspace. This paper outlines an approach that uses recorded surveillance data and intended flight paths to estimate the probability of NMAC. The method takes a geometric approach that is computationally more efficient than direct Monte Carlo simulation. Such a method could have broad use for safety assessment, policy making, airspace planning, and alternatives analysis.