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\sum_{n\neq a} p_n\frac{p_a}{1-p_n}=p_b\frac{p_a}{1-p_b}+p_c\frac{p_a}{1-p_n}+p_n\frac{p_d}{1-p_n}+p_n\frac{p_e}{1-p_n}
\sum_{n\neq a} p_n\frac{p_a}{1-p_n}=p_b\frac{p_a}{1-p_b}+p_c\frac{p_c}{1-p_n}+p_n\frac{p_d}{1-p_n}+p_n\frac{p_e}{1-p_n}
\sum_{n\neq a} p_n\frac{p_a}{1-p_n}=p_b\frac{p_a}{1-p_b}+p_\frac{p_c}{1-p_n}+p_n\frac{p_d}{1-p_n}+p_n\frac{p_e}{1-p_n}
\sum_{n\neq a} p_n\frac{p_a}{1-p_n}=p_\frac{p_a}{1-p_b}+p_n\frac{p_c}{1-p_n}+p_n\frac{p_d}{1-p_n}+p_n\frac{p_e}{1-p_n}
\sum_{n\neq m,a}\sum_{m\neq a} p_m\frac{p_n}{1-p_m}\frac{p_a}{1-p_m-p_n}+