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This paper presents a geometry-based three-dimensional Probability of Line of Sight <inline-formula> <tex-math notation="LaTeX">$(P_{\mathrm {LoS}})$ </tex-math></inline-formula> model for generic urban environments. The existing <inline-formula> <tex-math notation="LaTeX">$P_{\mathrm {LoS}}$ </tex-math></inline-formula> models are mostly empirical, based on measurements or ray-tracing simulations at specific environments. To enable Unmanned Aerial Vehicle (UAV) communication in various environments, it is urgently necessary to develop an analytical model with high parameter scalability. Through introducing the ITU model that describes a built-up environment with three parameters, we derive a closed-form <inline-formula> <tex-math notation="LaTeX">$P_{\mathrm {LoS}}$ </tex-math></inline-formula> model with the inputs of city built-up parameters, UAV altitude, elevation <inline-formula> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> and azimuth <inline-formula> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> angles between UAV and User Equipment (UE). Furthermore, we develop a geometry-based simulator to validate the proposed analytical model. The results show good agreements between the simulated results, analytical results, and 3GPP <inline-formula> <tex-math notation="LaTeX">$P_{\mathrm {LoS}}$ </tex-math></inline-formula> measurements. We demonstrate that the existing models provide less accurate results, which calls for re-evaluating the use cases and performance of UAV-mounted communication equipment in urban environments.