To improve the practicality, data-driven techniques of predicting the wind power generation and its uncertainty still need to address three technical challenges, uplifting the prediction accuracy via inventing an emerging data analytics mechanism, flexibly scaling up the prediction resolution from the data sampling resolution, and preventing invalid probabilistic prediction results. This study is thus motivated to investigate an advanced prediction method enabling highly accurate and valid probabilistic wind power predictions as well as the capability of a resolution scale-up. The long short term memory (LSTM) network combined with an attention-assisted ordinary differential equation network (AODEN), LSTM-AODEN, is developed for the first time in the literature to produce a novel deep network architecture for probabilistic wind power predictions via leveraging advantages of deep learning and ordinary differential equations. In the LSTM-AODEN, a two-stage training scheme, which sequentially develops one median prediction model and one multi-interval length prediction model, is proposed to fully eliminate quantile crossings and guarantee the validity of prediction results. Six evaluation metrics in computational experiments verify that the proposed LSTM-AODEN method leads to overall highly accurate and fully valid results of the point prediction, interval prediction, and quantile prediction compared to several classes of state-of-the-art probabilistic prediction methods. Meanwhile, the proposed method is proved to offer a unique capability of generating higher-resolution probabilistic wind power prediction results, which is gained from the AODEN, indicated by the lowest prediction errors.