Bidirectional path tracing (BDPT) can be accelerated by selecting appropriate light sub-paths for connection. However, existing algorithms need to perform frequent distribution reconstruction and have expensive overhead. We present a novel approach, SPCBPT, for probabilistic connections that constructs the light selection distribution in sub-path space. Our approach bins the sub-paths into multiple subspaces and keeps the sub-paths in the same subspace of low discrepancy, wherein the light sub-paths can be selected by a subspace-based two-stage sampling method, i.e., first sampling the light subspace and then resampling the light sub-paths within this subspace. The subspace-based distribution is free of reconstruction and provides efficient light selection at a very low cost. We also propose a method that considers the Multiple Importance Sampling (MIS) term in the light selection and thus obtain an MIS-aware distribution that can minimize the upper bound of variance of the combined estimator. Prior methods typically omit this MIS weights term. We evaluate our algorithm using various benchmarks, and the results show that our approach has superior performance and can significantly reduce the noise compared with the state-of-the-art method.