Accurate probabilistic prediction for intention and motion of road users is a key prerequisite to achieve safe and high-quality decision-making and motion planning for autonomous driving. Typically, the performance of probabilistic predictions was only evaluated by learning metrics for approximation to the motion distribution in the dataset. However, as a module supporting decision and planning, probabilistic prediction should also be evaluated from decision and planning perspective. Moreover, the evaluation of probabilistic prediction highly relies on the problem formulation variation and motion representation simplification, which lacks a summary in a comprehensive framework. To address such concerns, we provide a systematic and unified framework for the analysis of three under-explored aspects of probabilistic prediction: problem formulation, representation simplification and evaluation metric. More importantly, we address the omitted but crucial problems in the three aspects from decision and planning perspective. In addition to a review of learning metrics, metrics to be considered from planning perspective are highlighted, such as planning consequence of inaccurate and erroneous prediction, as well as violations of predicted motions to planning constraints. We address practical formulation variations of prediction problems, such as decision-maker view and blind view for viewpoint, as well as reactive prediction for interaction, so that decision and planning can be facilitated.