Although recent studies have proposed seizure detection algorithms with good sensitivity performance, there is a remained challenge that they were hard to achieve significantly short detection latency in real-time scenarios. In this manuscript, we propose a novel deep learning framework intended for shortening epileptic seizure detection latency via probabilistic prediction. We are the first to convert the seizure detection task from traditional binary classification to probabilistic prediction by introducing a crossing period from seizure-oriented EEG recording and proposing a labeling rule using soft-label for crossing period samples. And, a novel multiscale STFT-based feature extraction method combined with 3D-CNN architecture is proposed to accurately capture predictive probabilities of samples. Furthermore, we also propose rectified weighting strategy to enhance predictive probabilities, and accumulative decision-making rule to achieve significantly shorter detection latency. We implement the proposed framework on two prevalent datasets -- CHB-MIT scalp EEG dataset and SWEC-ETHZ intracranial EEG dataset in patient-specific leave-one-seizure-out cross-validation scheme. Eventually, the proposed algorithm successfully detected 94 out of 99 seizures during crossing period and 100% seizures detected after EEG onset, averaged 14.84% rectified predictive ictal probability (RPIP) errors of crossing samples, 2.3 s detection latency, 0.08/h false detection rate (FDR) on CHB-MIT dataset. Meanwhile, 84 out of 89 detected seizures during crossing period, 100% detected seizures after EEG onset, 16.17% RPIP errors, 4.7 s detection latency, and 0.08/h FDR are achieved on SWEC-ETHZ dataset. The obtained detection latencies are at least 50% shorter than state-of-the-art results reported in previous studies.