I sent you a response PM with a more in-depth explanation before reading this :x

Just let me know if what I sent was helpful. :)

Basically they set Black Flag to "Rainy/Afternoon" and bake what all the probes look like for that, then for all combinations of other times of day and weathers. Then, if say it's the afternoon and turning from clear to rainy in the game, they'll just blend between "Clear/Afternoon" and "Rainy/Afternoon". So all they had to do was look up two probes for each area and blend between them, which is quite cheap.

Whereas in Far Cry 3 they used a pre-computed radiance transfer function, which takes a given static area and calculates "If you have light here, then it's going to bounce around like this". So they could use whatever lighting they wanted and this function would produce the correct bounces for each probe. But this takes more time to compute than just looking up a texture essentially, and so they ditched that for Black Flag.

All solved. THANK YOU EVERYONE! Frentic, Mr. Hodge, and especially Styves !! <3!