Global navigation satellite systems (GNSS) station-based Precipitation Nowcasting aims to predict rainfall within the next 0-6 hours by leveraging a GNSS station's historical observations of precipitation, GNSS-PWV, and related meteorological variables, which is crucial for disaster mitigation and real-time decision-making. In recent years, time-series forecasting approaches have been extensively applied to GNSS station-based precipitation nowcasting. However, the highly imbalanced temporal distribution of precipitation, marked not only by the dominance of non-rainfall events but also by the scarcity of extreme precipitation samples, significantly limits model performance in practical applications. To address the dual imbalance problem in precipitation nowcasting, we propose a continuous probability modeling-based framework, RainBalance. This plug-and-play module performs clustering for each input sample to obtain its cluster probability distribution, which is further mapped into a continuous latent space via a variational autoencoder (VAE). By learning in this continuous probabilistic space, the task is reformulated from fitting single and imbalance-prone precipitation labels to modeling continuous probabilistic label distributions, thereby alleviating the imbalance issue. We integrate this module into multiple state-of-the-art models and observe consistent performance gains. Comprehensive statistical analysis and ablation studies further validate the effectiveness of our approach.