Adaptive Random Testing (ART) methods are Software Testing methods which are based on Random Testing, but which use additional mechanisms to ensure more even and widespread distributions of test cases over an input domain. Restricted Random Testing (RRT) is a version of ART which uses exclusion regions and restricts test case generation to outside of these regions. RRT has been found to perform very well, but its use of strict exclusion regions (from within which test cases cannot be generated) has prompted an investigation into the possibility of modifying the RRT method such that all portions of the Input Domain remain available for test case generation throughout the duration of the algorithm. In this paper, we present a probabilistic approach, Probabilistic ART (PART), and explain two different implementations. Preliminary empirical data supporting the methods is also examined.