Our 3-year-old home in Phoenix has hairline cracks at the bottom of the 1x4 trim boards adjacent to the exterior door jambs. These cracks extend an inch or two above the bottom of the board. One of the boards contacted a concrete slab (doorstep) so I sawed off 1/8" or so to prevent moisture from wicking up the endgrain. But others of these trim boards have cracks and don't contact concrete.

The cracks are too narrow to effectively force caulk into them. Can you suggest any fix for the cracks before repriming and repainting? Seems to me I need a liquid or syrupy filler of some kind.