Climate events that shatter previous records by large margins are a threat to society because critical infrastructure is often not designed to withstand such events. Climate change is expected to increase the probability of such events happening, but quantifying event probabilities is challenging due to natural variability and limited data availability, especially in observations and for events that would be "impossible" without climate change. Here, we quantify the changing probability of record shattering precipitation events in climate models using extreme value statistics. We show that CMIP6 models forced with SSP3-7.0 project much higher probability of record shattering extreme precipitation in a changing climate relative to a stationary climate by the end of the century. This holds for almost all the global land, in line with the expected intensification of extreme precipitation. For vulnerable regions in the tropics, the projected probability of shattering precipitation records anywhere in the region in a 5-year period exceeds 50% in the high warming SSP3-7.0 scenario. We demonstrate that increasing variability is an essential driver of near-term increases in precipitation record shattering probability. Overall, our results provide estimates of probabilities and intensities of unseen record shattering precipitation events in a warming world that are crucial to inform risk assessment and adaptation policies.