e.g. 40% shield versus 80% crit chance results in 80% crit chance and 20% shield chance and 0% normal hit

well what are the odds

the dmg is adjusted accordingly with surge or if shielded with absorp and after that it goes through the armor rating

(if theres no crit or no shield then there will be just normal dmg)

Besides the fact that 80% crit chance (unless some specific abilities) are a bit over the top, it is even worse:

Let's stay with 40% shield chance and 40% crit chance (more reasonable values). Crit happens regardless of shielded or non shielded attacks. Then you have 40% chance to crit. On the remaining 60% you have 40% chance to shield the attack. That is 40% * 60% = 24% shield chance and 36% normal hit.

with armor rating being the only tool to reduce yellow dmg (except several self buffs)

but do not expect them be comulative

e.g. invincible (40% dmg reduce), shield (25%) and if specced the self heal (15%) wont give u 80% dmg reduce

If the effects can apply all the time you would have 40% damage reduce and then of the remaining damage another 25% (25% *60% = 15%) so a sum of 55% now and of the remaining 45% you heal 15% (45% * 15% = 6.75%) so you're effective mitigation would be 40% + 15% + 6.75% = 62.75%.