Connected vehicles are becoming progressively capable of collecting, processing, and sharing data, which leads to a growing concern about privacy in the automotive domain. However, research has shown that although users are highly concerned about their privacy, they usually find it difficult to configure privacy settings. This is because the privacy context, which represents the privacy circumstance a driver faces during the privacy policy creation, is highly complex. To create custom privacy policies, drivers must consider the privacy context information, such as what service is requesting data from which vehicle sensor, or what privacy countermeasures are available for vehicles and satisfy certain privacy properties. This easily leads to information and choice overhead. Therefore, we propose the novel ontology-based privacy context model, CV-Priv, for the modeling of such privacy context information for creating custom privacy policies in the automotive domain. In this paper, we analyze the design requirements for a privacy context model based on challenges drivers might face during the privacy policy creation phase. We also demonstrate how CV-Priv can be utilized by context-aware systems to help drivers transform their fuzzy privacy requirements into sound privacy policies.