Cumulative conditional probability P(f_i|I) of SPE occurring in relation to solar flare. Different SPE thresholds are indicated by different colours, as specified in the legend. The SPE statistic (coloured symbols) is collected in nine logarithmic bins of the SXR peak flux, I, from the M1 class to the X32 class. The error bars represent one standard deviation. Coloured lines denote lognormal CDF fits with their uncertainties. The extrapolated probability of P(f₈₀₀ > 10⁸|I) roughly corresponding to the ESPE of 993/4 CE is shown in red along with its 68% credible interval (CrI; see Sect. 3.2). The bolometric energy (top abscissa) is estimated from the SXR peak fluxes using Equation S1.