Accurate short-term prediction of individual residential load is essential for various applications and low- voltage grid stakeholders. Distribution system operators can utilize these forecasts in grid simulations, operation planning, and to anticipate unusual or varying consumption in certain neighborhoods, which can help to avoid congestions caused by peaks. Furthermore, these predictions can be used to optimize the low-voltage grid for renewable energy sources and potential battery storage. Due to the highly stochastic nature of household consumption, point forecasting is not optimal. We apply state-of-the-art probabilistic methods from other applications, and we propose a novel probabilistic global approach. It is based on a selection of similar normalized household consumption time series, which are then used to compute empirical quantiles. The proposed method has been evaluated on two different open datasets from different countries, and it outperforms state-of-the-art models in both cases. It has also been applied to a private Belgian dataset. In all three cases, the proposed method consistently outperforms the state-of-the-art methods on highly stochastic and changing households, i.e., households experiencing concept drift. This method is scalable, with low computational requirements, requires only seven days of historical data of the target household to make predictions and does not require household-specific or weather information.