In this paper, a general framework, called probability-based solution (PBS), is proposed to balance the trade-off between the accessibility (in terms of the success probability to find a route reaching the destination) and the performance (in terms of spectral efficiency, outage probability or energy consumption) of distributed routing schemes in multi-hop wireless networks. In the PBS, the candidate nodes (receivers) in each hop are first separated into two groups based on a direction either diverging from, or converging to, the direct line between the source and destination. Then, one of the best nodes from the two groups is selected according to a carefully-defined probability by considering the uncertainty in the subsequent hops. The simulation results demonstrate that integrating the proposed PBS with conventional distributed routing schemes can significantly improve the accessibility and effectively guarantee other system performance. Moreover, the PBS can also be combined with facing routing to solve the connectivity hole problem.