My son and I have been stalked a couple of times, that we know of. Rule of thumb, is if you see a deer there is probably a cougar stalking it. We were riding the Santa Susanas one morning and came upon a cub on the trail. That is sure trouble so we walked backward until out of sight and GTFO. Another time a buddy and I were descending a trail and I startled a cougar lounging on an overhang. My buddy was second and the cougar ready to pounce so my buddy got off his bike, put it between him and the cougar, and screamed bloody murder so I shined my lights in his eyes. As it scrambled off we could see it was over 8 feet nose to tail.
Another time we were backpacking in the Rockies and one morning right after we cooked breakfast a good size cougar just moseyed into camp, smelled our dishes and went along our way. Looked at us like we were idiots. We were stunned.