In a convex hexagon, Diagonal intersect at interior point of an hexagon. 
In a convex hexagon two diagonal are drawn at random. The probability that the
diagonal intersect at an interior point of an hexagon is

$\bf{Attempt}$ I have a doubt,
Diagonal of Convex hexagon always intersect at interior of an hexagon. So probability is $1$
But answer is given as $\displaystyle \frac{5}{12}$
Please clear my doubt., Thanks

Hint
I am considering that a vertex is not an interior point.

Consider just those black points as an interior point. 
Remember that we have $9$ diagonals. Looking to the answer, the statement is 
also considering that any pair of diagonals have a intersection, even if it happens at an exterior.
Can you finish?
