In this work, a mathematical framework to evaluate the performance of a finite, three dimensional (3D) unmanned aerial vehicle (UAV) network in the presence of interference is developed. The framework builds upon stochastic geometry tools and specifically the binomial point process (BPP) for the spatial distribution of the UAVs. A UAV base station (UAV-BS) reference receiver is located at the center of a sphere and communicates with the nearest transmitting UAV node, whose distance from the UAV-BS reference receiver is either fixed or random. The reverse link suffers from the presence of a single dominant interferer, whose location is random within the sphere. Closed-form expressions are derived for statistical metrics of the signal-to-interference ratio (SIR) for two scenarios, namely for fixed or random location of the desired transmitting node. Then, the impact of the location of the transmitting node on the coverage probability (CP) is studied while the average error probability and the ergodic capacity have been also analytically investigated. Finally, the theoretical results are numerically evaluated and compared to simulation to reveal some useful insights.