News recommender systems aim to provide personalized news reading experiences for users based on their reading history. Behavioral science studies suggest that screen-based news reading contains three successive steps: scanning, title reading, and then clicking. Adhering to these steps, we find that intra-news entity interest dominates the scanning stage, while the inter-news entity interest guides title reading and influences click decisions. Unfortunately, current methods overlook the unique utility of entities in news recommendation. To this end, we propose a novel method called IP2 to probe entity-guided reading interest at both intra- and inter-news levels. At the intra-news level, a Transformer-based entity encoder is devised to aggregate mentioned entities in the news title into one signature entity. Then, a signature entity-title contrastive pre-training is adopted to initialize entities with proper meanings using the news story context, which in the meantime facilitates us to probe for intra-news entity interest. As for the inter-news level, a dual tower user encoder is presented to capture inter-news reading interest from both the title meaning and entity sides. In addition to highlighting the contribution of inter-news entity guidance, a cross-tower attention link is adopted to calibrate title reading interest using inter-news entity interest, thus further aligning with real-world behavior. Extensive experiments on two real-world datasets demonstrate that our IP2 achieves state-of-the-art performance in news recommendation.