Some Statistical Software Testing approaches rely on sampling the feasible paths in the control flow graph of the program; the difficulty comes from the tiny ratio of feasible paths. This paper presents an adaptive sampling mechanism called EXIST for Exploration/eXploitation Inference for Software Testing, able to retrieve distinct feasible paths with high probability. EXIST proceeds by alternatively exploiting and updating a distribution on the set of program paths. An original representation of paths, accommodating long-range dependencies and data sparsity and based on extended Parikh maps, is proposed. Experimental validation on real-world and artificial problems demonstrates dramatic improvements compared to the state of the art.