Inclusion probability under successive PPS draws: $z_3+\sum_{i\ne3}z_iz_3/(1-z_i)$

A probability proportional to size (PPS) without replacement sample of size 2 is to be drawn from a population of $N=3$ units. Let $z_1=1/4$, $z_2=1/4$, $z_3=1/2$. The $i$-th unit is selected with probability $z_i$, $i=1,2,3$. If the first unit selected is $i$, then the $j$-th unit is selected for inclusion in the sample with probability $z_j/(1-z_i)$, $j\ne i$. Then, the probability that the third unit in the population is included in the sample is given by: