Information Partition and Common Knowledge
The situation is not described by $K_A(K_B(3))$. $A$ does not know that the draw was 3, and hence does not know that $B$ thinks it is in the set $K_B(3)$. What $A$ does know is that the draw
is in set $K_A(3)$, hence $A$ thinks $B$ should have narrowed it down to $K_B(K_A(3))$.