Time for everyone's favorite thing, math!
Here comes a formula. Are you ready?
What is all of this Le Poo Poo?
HPmax is the Pokemon's maximum HP.
HPcurrent is the Pokemon's current HP.
rate is the Pokemon's catch rate. Giratina's is 3.
bonusball is catch modifiers on PokeBalls. I get to that later.
bonusstatus is a status bonus. Freeze has a value of 2, and 1.5 for paralysis, poison, and burn.
and on red pixel
Since you said "Pixel", I'm going to assume it has one pixel of HP left in the HP bar. After measurements, we can tell that the HP bar is 48 pixels long on a DS screen. With one pixel, this means Giratina has anywhere from 1 HP to 1/48th of its maximum HP at Level 47 (212 with 31 IVs, 198 with 0 IVs.).
Essentially, this means Giratina has anywhere from 1 to 5 HP left. (Same from 0-31 IVs)
I'll save you the math:
Red HP Capture Rates:
Poke Ball/Premiere Ball with 5 HP (Identical): 2.95
Poke Ball/Premiere Ball with 1 HP: 2.99
Great Ball with 5 HP: 4.43
Great Ball with 1 HP: 4.48-4.49
Ultra Ball with 5 HP: 5.90-5.91
Ultra Ball with 1 HP: 5.97-5.98
Dusk Ball with 5 HP: 10.32-10.33
Dusk Ball with 1 HP: 10.46-10.47
For the Poke Ball calculations and first Great Ball calculations, 0 IV calculations were slightly less than their 31 IV counterparts. So they will not be included separately.
Full HP Capture Rates:
Poke Ball/Premiere Ball: 1
Great Ball: 1.5
Ultra Ball: 2
Dusk Ball: 3.5
But Le Skeeter Johnson!!! How are the catch rates lower than Giratina's actual catch rate?!
This is due to how the formula is calculated. Here's a sample equation, with HPmax being "x", HPcurrent being "x" as well since it as at full HP, and rate being 3:
3(3x - 2x)/3x
This is how the formula works, and it is Game Freak's decision to make it this way. This could possibly be a more difficult way to catch Pokemon, but nobody can be sure.
Source 1 | Source 2 | HP Bar Source