Electric vehicles (EVs) have attracted more and more attention around the world due to their excellent carbon reduction capability. However, EVs have always had the challenge of "range anxiety." One possible way to solve this challenge is the state of charge (SOC) probabilistic estimation. It gives the estimated SOC value, the upper and lower bounds of SOC during the driving. The upper/lower bound reflects the maximum possible upper/lower SOC value, which can help optimistic/prudent users make reasonable decisions. This article has proposed a novel state-of-the-art probabilistic estimation method based on natural gradient boosting (NGBoost). The performance of the proposed method is validated on a public dataset and the self-made experimental datasets, which contain various battery chemistries, operation conditions, and ambient temperatures. For probabilistic estimation, the results show that the estimated intervals can better contain the true values than only the deterministic estimation, giving sufficient consideration and richer information. For deterministic estimation, compared with the existing methods, the proposed method can achieve better mean errors. This work highlights the promise of reducing "range anxiety" based on state-of-charge probabilistic estimation with NGBoost.