Modern evaluation of learning pipelines often reduces to downstream accuracy, leaving open the question of why tasks succeed or fail. TriProbe addresses this gap with a multi-level probing framework for explainable diagnosis of task separability. Rather than treating models as black boxes, TriProbe traces how separability evolves across inputs, learned features, and final classifiers. It decomposes multi-task problems into binary subtasks and applies three complementary probes: a Foundational Probe on input spaces, a Latent Probe on feature representations, and a Final Probe on classifier outputs. Using Maximum Fisher's Discriminant Ratio as a principled separability metric, TriProbe identifies bottlenecks and affected task pairs. Experiments on the Roshambo sEMG benchmark show how TriProbe reveals hidden breakdowns, guiding data collection, validation, and architecture design.