$H(X|Y)={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^{m}p(x_i,y_j)\cdot I(x_i|y_j)}}$

where $X=\left\{x_1\mathrm{,}\dots ,x_n\right\}$ is the set of events $x_i\left(i=\mathrm{1,}\dots ,n\right)$, $Y=\left\{y_1\mathrm{,}\dots ,y_m\right\}$ is the set of events $y_j\left(j=\mathrm{1,}\dots ,m\right)$, $I\left(x_i|y_j\right)$ is the conditional information content of $x_i$ given $y_j$, and $p\left(x_i,y_j\right)$ the joint probability that both events occur