The "8 ever 9 never" advises finessing against the Queen with an 8-card fit, and attempting to drop the Queen with a 9-card or better fit.
Finessing against the Queen offers a 50% chance of success. Cashing the Ace (or King) before finessing avoids losing to a singleton Queen offside, a 2.83% chance. However, the safety play prevents you from picking up Qxxxx onside, a 1.96% chance. So the safety play provides a 50.87% chance to avoid losing to the Queen. In an 8-card fit, playing to drop the Queen works when the Queen is singleton (a 5.66% chance), or doubleton (a 27.14% chance), a combined 32.8% chance. With an 8-card fit, finessing with the safety play offers a 20% better chance of success than playing to drop the Queen.
With a 9-card fit, finessing offers a 50% chance of success. Cashing the Ace (or King) and then finessing is a safety play to avoid losing to a singleton Queen offside, a 6% chance. This safety play and then finessing offers a 56% chance of avoiding losing to the Queen. Playing for the drop wins when the suit break 2-2, (a 40% chance), or the suit breaks 3-1 with a singleton Queen (a 12% chance), or the suit break 4-0 and the Queen is onside for a marked finesse (almost a 5% chance). These combinations provide almost a 58% chance for an attempt to drop the Queen to avoid losing a trick. Playing for the drop offers a 1.7% better chance than cashing the Ace or King and then finessing. So without any additional information it is better to play to drop the Queen with a 9-card fit. However, the auction and play may help declarer infer one hand has more Vacant Spaces than another hand. This may tip the balance in favor of finessing.
The tables below provide probabilities for potential splits in the suit. The first table provides the odds of splits of the missing 5 cards when playing in an 8-card fit.
The table below provides the odds of splits of the missing 4 cards when playing in a 9-card fit.
If you have an 11-card fit missing the King, similar logic applies. Finessing against the King offers a 50% chance of success. Playing the Ace, attempting to drop a singleton King, offers a 52% chance.