very very low. but exceedingly high affinity of CO.

This is based on the structural differences between CO and CO2, and shape of the binding sites in haemoglobin.
CO2 is too long to fit in.

As far as I can remember, CO better than O2 better than H2O much better than CO2.

Bond lengths (all in angstrom, and not very accurate):
CO : C-O 1.20
O2 : O-O 1.52
H2O: O-H 0.94, 0.94 doesn't have to x2, the O binds, H only projecting, but H is small
CO2: C-O 1.20, 1.20 x 2 = 2.4, and O atom is big

You can go to PDBsum, ENTER PDB code 1b86, then, at lower right, click on the icon "surface", you will able to see a binding site is big enough for O2, better with CO, H2O is OK, CO2 has less chance to get in when compete with O2.