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.