Probability with volumes of a cuboid

Question

Suppose you are allowed to choose any 6 random numbers from ${1,2,3,\cdots,999}$. Let three of them be $a_1,a_2,a_3$ then the remaining three be $b_1,b_2,b_3$. Then what is the probability that box with dimensions of $a_i$ fits into box of $b_i$. Note that the box can be rotated before placing. Now i took numbers numbers $1,2,3,4,5,6$. Now I saw that for all possible $20$ cases $5$ are favorable. But how do i prove that its true for general $i,i+1,i+2,i+3,i+4,i+5,i+6$ also any random collection of $6$ numbers. Is the induction the way? Or any other way? Thanks