Conversational recommender systems (CRSs) capture a user preference through a conversation. However, the existing CRSs lack capturing comprehensive user preferences. This is because the items mentioned in a conversation are mainly regarded as a user preference. Thus, they have limitations in identifying a user preference from a dialogue context expressed without preferred items. Inspired by the characteristic of an online recommendation community where participants identify a context of a recommendation request and then comment with appropriate items, we exploit the Reddit data. Specifically, we propose a Contrastive Learning approach for Injecting Contextual Knowledge (CLICK) from the Reddit data to the CRS task, which facilitates the capture of a context-level user preference from a dialogue context, regardless of the existence of preferred item-entities. Moreover, we devise a relevance-enhanced contrastive learning loss to consider the fine-grained reflection of multiple recommendable items. We further develop a response generation module to generate a persuasive rationale for a recommendation. Extensive experiments on the benchmark CRS dataset show the effectiveness of CLICK, achieving significant improvements over state-of-the-art methods.