There is a bit to learn from this one.
Any vehicle that doesn't signal turns deserves extra caution, and I was expecting this car to slam into you. As soon as the hazard is identified, an alerting brake flash followed by a mirror check so you know your options beforehand is a good habit to get into.
On wet roads it is advisable to stay in a lower gear so you can slow down with engine compression only in many cases.
Use both brakes. Most stopping power is up front, and as you decelerate even more weight shifts up front. Stopping only the wheel that is losing weight is a losing proposition. Think of stopping a belt sander with your hand: the harder you push, the quicker it stops, but you can glide your hand on the sanding belt with minimal weight all day long (ouch) without stopping it at all.
The good thing is that you stayed on the brake. MSF teaches this with the induced lockup: stay on the brake till you stop. Release a locked wheel and it discovers it is on moving ground and tries to catch up. Usually by kicking out to the side, same as fishtailing with wheelspin.
Proper technique is the issue, tires can stop just fine. There is plenty of traction, you just have to use it right (
traction pie).
