In this paper, we consider a radar network for sensing ground targets where radars mounted on unmanned aerial vehicles (UAVs) that fly at a certain altitude are randomly distributed according to a two-dimensional homogeneous Poisson point process (HPPP). For such a sensing network, we derive the distribution of the radar interference using a stochastic geometry based analysis. In particular, when Swerling I model is considered for radar cross-section area (RCS) for the target, we derive the Laplace transform of the radar interference. Here, to avoid a strong interference between neighboring radars, a guard zone is introduced within which the UAV radar transmission around the permitted active radar is inhibited. As the radar performance metric, we derive the successful ranging probability (SRP) of a given radar by exploiting the Laplace transform of radar interference. Using our analytical results, which are verified by computer simulations, we argue that the radar network design parameters such as the radius of the guard zone and the density of the active radars can be optimized.