Accurate short-term prediction of overhead line (OHL) transmission ampacity can directly affect the efficiency of power system operation and planning. Any overestimation of the dynamic thermal line rating (DTLR) can lead to lifetime degradation and failure of OHLs, safety hazards, etc. This paper presents a secure yet sharp probabilistic prediction model for the hour-ahead forecasting of the DTLR. The security of the proposed DTLR limits the frequency of DTLR prediction exceeding the actual DTLR. The model is based on an augmented deep learning architecture that makes use of a wide range of predictors, including historical climatology data and latent variables obtained during DTLR calculation. Furthermore, by introducing a customized cost function, the deep neural network is trained to consider the DTLR security based on the required probability of exceedance while minimizing deviations of the predicted DTLRs from the actual values. The proposed probabilistic DTLR is developed and verified using recorded experimental data. The simulation results validate the superiority of the proposed DTLR compared to state-of-the-art prediction models using well-known evaluation metrics.