Random in 3-4-5

ABC is a right triangle with sides 3, 4 and 5. There are 3 random points (D, E and F) on the three sides assumed to be uniformly distributed: D on AB, E on BC and F on AC. Draw the three lines segments from vertices to these random points: AE, BF and CD. The intersection of AE and BF is the point P. The intersection of AE and CD is the point Q. The intersection of CD and BF is the point R. What is expected area of the PQR triangle? Answer format: decimal number rounded to 10 digits after the decimal point.