Using a limited number of probes has always been a focus in interface-level network topology probing to discover complete network topologies. Stop-set-based network topology probing methods significantly reduce the number of probes sent but suffer from the side effect of incomplete topology information discovery. This study proposes an optimized probing method based on stop probabilities (SPs) that builds on existing stop-set-based network topology discovery methods to address the issue of incomplete topology information owing to multipath routing. The statistics of repeat nodes (RNs) and multipath routing on the Internet are analyzed and combined with the principles of stop-set-based probing methods, highlighting that stopping probing at the first RN compromises the completeness of topology discovery. To address this issue, SPs are introduced to adjust the stopping strategy upon encountering RNs during probing. A method is designed for generating SPs that achieves high completeness and low cost based on the distribution of the number of RNs. Simulation experiments demonstrate that the proposed stop-probability-based probing method almost completely discovers network nodes and links across different regions and times over a two-year period, while significantly reducing probing redundancy. In addition, the proposed approach balances and optimizes the trade-off between complete topology discovery and reduced probing costs compared with existing topology probing methods. Building on this, the factors influencing the probing cost of the proposed method and methods to further reduce the number of probes while ensuring completeness are analyzed. The proposed method yields universally applicable SPs in the current Internet environment.