Since the content delivery unit over Information-Centric Networking (ICN) has shifted from files to the segments of a file named chunks, solely either file-level or chunk-level request probability is insufficient for ICN cache management. In this paper, a Request Expectation Index (RXI) based cache replacement algorithm for streaming content delivery is proposed. In this algorithm, RXI is introduced to serve as a fine-grained and unified estimation criteria of possible future request probability for cached chunks. RXI is customized for streaming content delivery by adopting both file-level and chunk-level request probability and considering the dynamically varied request status at each route as well. Compared to prior work, the proposed algorithm evicts the chunk with the minimum expectation of future request to maintain a high cache utilization. Additionally, simulation results demonstrate that the RXI-based algorithm can remarkably enhance the streaming content delivery performance and can be deployed in complex network scenarios. The proposed results validate that, by taking fine-grained request probability and request status into consideration, the customized in-network caching algorithm can improve the ICN streaming content delivery performance by high cache utilization, fast content delivery, and lower network traffic.