A conservative design team C and an innovative design team I are asked to separately design a new product within a month. From past experience, we know:

i) The probability that team C is successful is $\frac{1}{2}$.

ii) The probability that one and exactly one team is successful is $\frac{5}{8}$.

iii) The probability that both teams are successful is $\frac{1}{4}$.

Conditioned on at least one team is successful, what is the probability that team C fails?