Probabilistic load forecasting (PLF) is of important value to grid operators, retail companies, demand response aggregators, customers, and electricity market bidders. Gaussian processes (GPs) appear to be one of the promising methods for providing probabilistic forecasts. In this paper, the log-normal process (LP) is newly introduced and compared to the conventional GP. The LP is especially designed for positive data like residential load forecasting little regard was taken to address this issue previously. In this work, probabilisitic and deterministic error metrics were evaluated for the two methods. In addition, several kernels were compared. Each kernel encodes a different relationship between inputs. The results showed that the LP produced sharper forecasts compared with the conventional GP. Both methods produced comparable results to existing PLF methods in the literature. The LP could achieve as good mean absolute error (MAE), root mean square error (RMSE), prediction interval normalized average width (PINAW) and prediction interval coverage probability (PICP) as 2.4%, 4.5%, 13%, 82%, respectively evaluated on the normalized load data.