Multi-goal path finding (MGPF) aims to find a closed and collision-free path to visit a sequence of goals orderly. As a physical travelling salesman problem, an undirected complete graph with accurate weights is crucial for determining the visiting order. Lack of prior knowledge of local paths between vertices poses challenges in meeting the optimality and efficiency requirements of algorithms. In this study, a multi-task learning model designated Prior Knowledge Extraction (PKE), is designed to estimate the local path length between pairwise vertices as the weights of the graph. Simultaneously, a promising region and a guideline are predicted as heuristics for the path-finding process. Utilizing the outputs of the PKE model, a variant of Rapidly-exploring Random Tree (RRT) is proposed known as PKE-RRT. It effectively tackles the MGPF problem by a local planner incorporating a prioritized visiting order, which is obtained from the complete graph. Furthermore, the predicted region and guideline facilitate efficient exploration of the tree structure, enabling the algorithm to rapidly provide a sub-optimal solution. Extensive numerical experiments demonstrate the outstanding performance of the PKE-RRT for the MGPF problem with a different number of goals, in terms of calculation time, path cost, sample number, and success rate.