Current conversational passage retrieval systems cast conversational search into ad-hoc search by using an intermediate query resolution step that places the user’s question in context of the conversation. While the proposed methods have proven effective, they still assume the availability of large-scale question resolution and conversational search datasets. To waive the dependency on the availability of such data, we adapt a pre-trained token-level dense retriever on ad-hoc search data to perform conversational search with no additional fine-tuning. The proposed method allows to contextualize the user question within the conversation history, but restrict the matching only between question and potential answer. Our experiments demonstrate the effectiveness of the proposed approach. We also perform an analysis that provides insights of how contextualization works in the latent space, in essence introducing a bias towards salient terms from the conversation.