Due to the vast electric vehicle (EV) penetration to distribution grid, charging load forecasting is essential to promote charging station operation and demand-side management.However, the stochastic charging behaviors and associated exogenous factors render future charging load patterns quite volatile and hard to predict. Accordingly, we devise a novel Diffusion model termed DiffPLF for Probabilistic Load Forecasting of EV charging, which can explicitly approximate the predictive load distribution conditioned on historical data and related covariates. Specifically, we leverage a denoising diffusion model, which can progressively convert the Gaussian prior to real time-series data by learning a reversal of the diffusion process. Besides, we couple such diffusion model with a cross-attention-based conditioning mechanism to execute conditional generation for possible charging demand profiles. We also propose a task-informed fine-tuning technique to better adapt DiffPLF to the probabilistic time-series forecasting task and acquire more accurate and reliable predicted intervals. Finally, we conduct multiple experiments to validate the superiority of DiffPLF to predict complex temporal patterns of erratic charging load and carry out controllable generation based on certain covariate. Results demonstrate that we can attain a notable rise of 39.58% and 49.87% on MAE and CRPS respectively compared to the conventional method.