The equality of two conditional probability Suppose that a company has had $70\%$ female applicants and $30\%$ male applicants since it was founded. We also assume that $70\%$ of all staff are female. 
Let $F$ denote female and $M$ denote male and $S$ denote the event that an applicant is successful.
The question is: Is $P(S|F)=P(S|M)$?
Here is my working but perhaps it is not correct.
By the conditional probability we have
$$
\begin{align*}
P(S|F)&=\frac{P(S\cap F)}{P(F)}=\frac{0.7}{0.7}=1\\
P(S|M)&=\frac{P(S\cap M)}{P(M)}=\frac{0.3}{0.3}=1
\end{align*}
$$
So $P(S|F)=P(S|M)$.

You're saying that given an applicant is female, they are guaranteed to get the job, and similarly for males. That is probably not true. $P(S\cap F)$ does not necessarily equal $0.7$. If there were $70$ female applicants of $100$ total applicants and $7$ females got the job then $P(S\cap F)=0.7\cdot0.1=0.07.$
We have
$$
\begin{align*}
P(S\mid F)&=\frac{P(F\mid S)\cdot P(S)}{P(F)}=\frac{0.7\cdot P(S)}{0.7}\\
P(S\mid M)&=\frac{P(M\mid S)\cdot P(S)}{P(M)}=\frac{0.3\cdot P(S)}{0.3}
\end{align*}
$$
From here the $P(S)$'s cancel and you can deduce the desired result.
