Intelligent assistants change the way people interact with computers and make it possible for people to search for products through conversations when they have purchase needs. During the interactions, the system could ask questions on certain aspects of the ideal products to clarify the users' needs. For example, previous work proposed to ask users the exact characteristics of their ideal items [27, 37] before showing results. However, users may not have clear ideas about what an ideal item looks like, especially when they have not seen any item. So it is more feasible to facilitate the conversational search by showing example items and asking for feedback instead. In addition, when the users provide negative feedback for the presented items, it is easier to collect their detailed feedback on certain properties (aspect-value pairs) of the non-relevant items. By breaking down the item-level negative feedback to fine-grained feedback on aspect-value pairs, more information is available to help clarify users' intents. So in this paper, we propose a conversational paradigm for product search driven by non-relevant items, based on which fine-grained feedback is collected and utilized to show better results in the next iteration. We then propose an aspect-value likelihood model to incorporate both positive and negative feedback on fine-grained aspect-value pairs of the non-relevant items. Experimental results show that our model is significantly better than state-of-the-art product search baselines without using feedback and those baselines using item-level negative feedback.