COBRA-PPM is a novel causal Bayesian inference architecture that combines causal Bayesian networks and probabilistic programming to perform interventional inference for robotic manipulation under uncertainty. Its functionality is demonstrated through high-fidelity Gazebo-based experiments, predicting manipulation outcomes with high accuracy (prediction accuracy: 88.6%) in a block stacking task and performing greedy suboptimal selection with a task success rate of 94.2%. Furthermore, sim2real transfer is demonstrated in a domestic robot, demonstrating its effectiveness in handling real-world uncertainty due to sensor noise and probabilistic behavior. This generalizable and scalable framework supports diverse manipulation scenarios and lays the foundation for future research at the intersection of robotics and causality.