A probability problem by Mayank Raj

There are $\binom{7}{3}$ ways of choosing which three balls go into box A, and there are $2^4$ ways of distributing the other four balls between boxes B and C. Since there are $3^7$ ways of distributing the balls altogether, the desired probability is $\frac{\binom{7}{3} 2^4}{3^7} \; = \; \boxed{0.2560585227}$