Conditional inclusion-exclusion with three events

Let $E_{1},E_{2},E_{3}$ and $E_{4}$ be four events such that $$P(E_{i}|E_{4})=\frac{2}{3}, i=1,2,3;\quad P\left(E_{i}\cap E_{j}^{c}|E_{4}\right)=\frac{1}{6}, i,j=1,2,3; i\neq j\quad\text{and}\quad P\left(E_{1}\cap E_{2}\cap E_{3}^{c}|E_{4}\right)=\frac{1}{6}$$ Then, $P(E_{1}\cup E_{2}\cup E_{3}|E_{4})$ is equal to