A super-Albert string is a sequence of characters using only letters $A$, $L$, $B$, $E$, $R$, and $T$ that also contains the string $ALBERT$ as a subsequence. Find the probability that a random length $10$ super-Albert string contains $ARE$ (Saketh’s last name) as a subsequence.
Note: A subsequence of a string $S$ is any string that can be made by removing characters $S$, without changing the order of any characters.