Dear Mrityunjay Tripathi

do you mean the multivariate continuous Dirichlet distribution (extended beta)?

If yes, then do not be wondering, since then for the cpdf the formula is a very complicated combination of gamma multidimensional integrals. Moreover this is a pd concentrated on the simplex formed by points with positive coordinates summing up to 1In the case of 3D, this is concentrated on the triangle

x+y+z=1, where x,y,z >0.

What would you do with such function F(a,b,c) which is zero fro all triples a,b,c, which sum up to value less than 1?

I suggest you to check the following urls which are very useful for you:

https://stats.stackexchange.com/questions/57262/implementation-of-dirichlet-cdf

http://ugrad.stat.ubc.ca/R/library/MCMCpack/html/dirichlet.html