This belongs to geometric probability.
AD:AB=AE:AC=2/3
Point p can only be in trapezoidal BCED,
What is the area ratio of triangle ADE to triangle ABC (2/3)? =4/9
∴? The area ratio of trapezoidal BCED to triangular ABC is 5/9.
Namely. The probability that the area of triangle PBC is less than S/3 is 5/9.