Geometrical Probability

$ABCDE$ is a convex pentagon with $\overrightarrow { AB } =2\overrightarrow { DC }$ and $3\overrightarrow { AE } =\overrightarrow { BC }$ . the diagonals $AD$ and $BE$ meet at $F$ .

If $P(E_{1})=|\frac { \overrightarrow { AF } }{ \overrightarrow { DF } } |,~P(E_{2})=|\frac { \overrightarrow { EF } }{ \overrightarrow { BF } } |$ , where $E_{1},E_{2},E_{3}$ are mutually exclusive and exhaustive events of an experiment then $P(E_{3})$ is

Note that $P(E_{i})$ denotes probability of event $E_{i}$