"Equal probability" refers to a situation where all possible outcomes have an even chance of happening. It means that each option or result has the same likelihood or likelihood as all others. Full definition
For this, properly constructed samples using equal probability of selection methods are required which are sufficiently large to investigate the issues raised in this paper. (link.springer.com)
Over the last decade, record highs were more than twice as common as record lows, whereas half a century ago there was a roughly equal probability of experiencing either of these. (insteading.com)
That they are uncertain cuts both ways; things might not turn out as badly as the models now suggest, but with equal probability, they could turn out worse. (archive.boston.com)