In drug development, biomarkers can be used to help select patients that are more likely to benefit from the treatment, and developing these biomarkers has associated milestones and risks. To allow for proper go/no-go decision making of biomarker development, we developed a Bayesian framework for calculating the predictive probability of success of biomarker development. Given the data observed in the 'training' phase, the proposed method estimates the probability of observing a successful validation of the biomarker in the 'validation' phase. We consider the settings of both single-arm studies and randomized two-arm studies. In both cases, data from the training phase was used to make inferences on efficacy parameters in both biomarker+ and biomarker- populations, which were then utilized to predict the probability that pre-specified PPV and NPV criteria can be met in the 'validation' phase.