Select numbers $a$, $b$, and $d$ between $0$ and $1$ independently and at random. Let $S=a+b+d$. Let $A$, $B$, and $D$ be the results when $a$, $b$, and $d$ respectively, are rounded to the nearest integer. Let $T$ be the result when $S$ is rounded to the nearest integer. What is the probability that $A+B+D=T$?