Spatial-temporal wind power prediction is of enormous importance to the grid-connected operation of multiple wind farms in the wind power system. However, most of the conventional methods are usually limited to predicting an individual wind farm's power, and thus lack enough effectiveness of wind power forecasting of multiple adjacent wind farms. This paper proposes a novel spatial-temporal wind power probabilistic prediction approach, named ZF-GCN-MHTQF, based on time zigzags and flexible convolution at graph convolutional network, point-wise loss function and the heavy-tailed quantile function. The proposed framework combines the advantages of time zigzags and flexible convolution at graph convolutional networks that can extract temporally conditioned topological information from multiple wind farms efficiently and incorporate the extracted topological information to predict wind power. At the same time, the proposed method incorporates the strengths of point-wise loss functions and heavy-tailed quantile functions which can effectively tackle the problem of the traditional multi-quantile regression and accurately capture the full conditional distribution information of wind power. In our experiments, two real-world wind power datasets from Australia are utilized to validate the proposed model. Numerical experiments demonstrate the effectiveness and robustness of the proposed method compared to the state-of-the-art spatial-temporal models.