Incarnation is not simply your thoughts; it's your entire subconsciousness. The reason why it can be considered passive would be that your subconscious thoughts dictate Incarnation, not your active thought. Simply having confidence in your own skills compared to another person will activate Incarnation.
Now, actually using Incarnation abilities such as Incarnation Barriers and such, those types of abilities require active thought, but the probability manipulation aspect is subconscious thought.
If a person enters battle believing in themselves and having self confidence, then it practically is passive.
If you need it, I just created a blog post just for subconscious/passive Incarnation feats:
https://vsbattles.fandom.com/wiki/User_blog:Xmark12/SAO:_Passive_Reality_Warping_Stuff
Anyways, Sinbad's precog doesn't look like it's combat applicable from its description, "As a Singularity Sinbad can see the threads of destiny and guide others along", but prove me wrong if it is. If it isn't though, Kirito's own analytical prediction/Hypersense seems to be superior, since it's stated to be a sort of 6th sense that allows him to react to danger. If Sinbad's precog is combat applicable though, then either way Hypersense would balance it out.
Power null from the looks of things also requires touch, and it's in-character for Kirito in this key to start from a distance and shoot projectiles before going in himself. Even if he is power null'd, it's only his Sacred Arts. Incarnation would still be available because in terms of verse equalization, Sacred Arts = Magoi and Incarnation =/= Sacred Arts.
As for his Dijin Equips, all of them are either countered by Kirito's own moveset or resisted (in the case of Mind Manipulation).
It also doesn't seem like Sinbad has an answer to Kirito's instant Mid regen, Incarnation Barriers, invisible Incarnation Blades, and various means of negating durability (turning Sinbad into a tree, reversing his age, creating blades inside of him).
Divine Protection is the deciding factor here though. If Sinbad gets 1-B protection, then obviously this match will be a stomp.
For now though, going Kirito.
