'08 Escape skipping on wet road?

I was out the other night, it had rained lightly so the road was wet. No puddles to speak of just wet. The car in front of me stopped quickly, so I hit my brake harder than usual. But the Escape didn't stop it (for a lack of a better word) skipped for about ten or so feet. Luckily, I didn't hit anyone. When I was clear in traffic and no one was around, I hit the brake to stop quickly and it happened again. I don't really know much about cars, is there an issue with the tires or the brakes or both?

The tires may be the original set but I'm not sure. It's an 2008 Escape with 40,000 miles.

Any help steering me in the right direction would be appreciated.