Example: You get hit with 1000 physical damage.

Your defensive stats are: 0 armour, 0 physical damage reduction, 80% of physical damage taken as fire damage, 90% fire resistance

Thus you would take 200 physical damage and 80 fire damage.

Does divine shield do anything in this example?

Because technically, 620 physical damage have been prevented in the scenario. However most of the originating physical damage was shifted to be taken as fire in the process and no "actual" physical damage was mitigated.