Frequently, clinical trials and observational studies involve event history data with multiple events. In such cases, the standard analysis methods compare hazard rates or transition intensities for particular events across groups. However, these methods do not provide direct inference about event probabilities, which are frequently of main scientific interest. In this work, we propose nonparametric two-sample tests for transition probabilities in general nonhomogeneous Markov multi-state models. The asymptotic null distributions of the tests are derived and the tests are shown to be consistent against any alternative hypothesis. The latter implies that the tests provide good power for detecting a difference even between crossing transition probability curves. Extensions to settings with clustering, such as multicenter studies and cluster-randomized trials, are also discussed. Simulation studies show good performance of the tests even with small sample sizes and under alternative hypotheses with crossing transition probability curves. Finally, the proposed tests are illustrated using real data from a randomized controlled trial on treatment of metastatic squamous-cell carcinoma.