Contextual models like BERT are highly effective in numerous text-ranking tasks. However, it is still unclear as to whether contextual models understand well-established notions of relevance that are central to IR. In this paper, we use probing, a recent approach used to analyze language models, to investigate the ranking abilities of BERT-based rankers. Most of the probing literature has focussed on linguistic and knowledge-aware capabilities of models or axiomatic analysis of ranking models. In this paper, we fill an important gap in the information retrieval literature by conducting a layer-wise probing analysis using four probes based on lexical matching, semantic similarity as well as linguistic properties like coreference resolution and named entity recognition. Our experiments show an interesting trend that BERT-rankers better encode ranking abilities at intermediate layers. Based on our observations, we train a ranking model by augmenting the ranking data with the probe data to show initial yet consistent performance improvements (The code is available at https://github.com/yolomeus/probing-search/ ).