Falling uair into knee is amazing. It's basically the new stomp to knee. It's far safer than raw knee because uair has a mere 9 frames on landing lag, and is likely safe even on shields unless it's powershielded. It easily registers as a true combo in training mode and it works at a huge variety of %s unlike most combos in this game which seem to only work at very strict %s. It also seems to work on pretty much everybody in the game, from Jigglypuff to Bowser.
The best part of it is the fact it lets Captain Falcon easily kill at % ranges where no one else can hope to do so without gimping. Like normally the Lucario matchup is a huge pain because once you get him to 100% he goes monster mode and you still can't kill him with a side B. But uair into knee combos and KILLS at a mere 63% from the center of FD. Furthermore it can kill even earlier if you have rage, and still manages to combo at 90% (although it will be less than this with rage).
So once you have Lucario or anyone else in the 60-90% range, suddenly Falcon has the power to punish even the tiniest mistake with a kill. Combine it with Falcon's incredible speed which lets him rush in from anywhere on the stage with a flying uair and you have a punishing beast.
The key to actually doing the combo is knowing the jump timings between the uair and the knee. The reason why this combo can work on such a large span of %s is because of Falcon's jump speed, and the ability to vary your jump height with shorthops, fullhops, and timing your double jump. At very low percents you can combo uair into shorthop knee, although this usually won't kill and is a waste of the Knee's freshness. At mid percents uair will combo into a simple fullhopped knee. At higher percents you will have to double jump and the timing is very % specific, for instance when your opponent just reaches %s where fullhopped knee won't land, you need to jump and them immediately double jump knee, while at high %s you'll need to double jump at the peak of your full jump.
Also where you hit them with your uair affects the combo too. Hitting them with it close up sends them slightly higher up while hitting them at a bit of a distance sends them up less but more forward. Usually you want to hit them close at low %s and farther at high %s but this varies depending on the character.
This combo will need a lot of practice to pull off in real battles especially since rage can mess with your calculations, so you just need to try it out a lot to get a feel for how to time your jumps for the knee.
Note that the %s vary a lot depending on the floatiness and weight of the opponent. Floaty characters like Puff are trickier to combo and have a smaller range of %s that the combo works at. Also short characters (also like Puff) are difficult to hit with uair and it may be completely impossible to hit them if they are crouching. This combo is mainly landed as a punish anyways though. If you just start jumping around with shorthopped uairs once they are at mid percents it will be very obvious and you will be punished in return.
Here are some example %s just to show the sheer range this combo works at (done on FD, no rage or DI factored and probably not completely precise):
Jigglypuff: Starts to combo at 23% (can string at any percent with single hit nair -> knee). Kills at 43%. No longer combos at 72% (might be possible with frame perfect timing).
Rosalina: Starts to combo at 27%. Kills at 48%. No longer combos at 81%. Also note hitting Luma causes extra hitlag and can mess up your combos (Sakurai why did you give her this annoying little thing).
Sheik: Starts to combo at 33%. Kills at 47%. No longer combos at 90%.
Bowser: Starts to combo at 39%. Kills at 66%. No longer combos at 112%.
So around 60% is where the combo starts to work and kill on everybody.
The only problem is doing shorthop fast fall uair in a real battle is really hard and not very practical on the 3DS. But it should be easy on the Wii U.
An alternative Knee combo that works on the 3DS is dthrow -> uair -> knee. This combo however only seems to work at very specific %s and on some characters it won't register as a true combo. In a real battle you only get one shot at it because if you miss the knee, you opponent will be too high of a %.
As an extra note, Falcon can combo single hit nair into grab/jab at ANY percent since the first hit of nair has a set knockback. So for people trying to find more Falcon approaches, short hop fast fall nair can be used as an aerial jab of sorts and you can use it to poke at defensive player's shields into grabs.