If you’ve seen them freeze before then they’d probably freeze. Even if they did run, it’s unlikely that they could outrun something like an eagle or a fox. It’s really important that you are with them (and close, not just in the same general area) at all times when they’re outside, as they really have no chance against large, wild predators that are experienced in catching wild rabbits. A domesticated animal would be an easy snack for a predator used to catching instinctive, wild animals.

How on earth could we possibly know how your rabbit would react to a predator?

We have wild rabbits that live in our backyard (well, they live in the blackberry bushes on the other side of our fence, but spend their days in our backyard grazing.) When our dogs are out they will freeze and hold still until the dogs move away, but if the dogs get too close they’ll bolt. That being said, they’re wild and I don’t know if those instincts translate to domesticated rabbits. My neighbor’s cats successfully catch wild rabbits on occasion so I wouldn’t assume your domestic pet would be any better at staying safe.
My advice, don’t put it to a test.

My previous bunnies lived outside and would encounter a cat every now and then in our backyard (they were in an enclosed hutch). They’d go crazy in their hutch running back and forth, thumping and hiding away.

It can be hard to know how your rabbits would respond. Our domesticated buns have differing levels of survival response to predators than their wild counterparts, while their senses may not be dimmed, they don’t always display the appropriate response.

For many prey animals the first response is to freeze. This allows the prey to observe the threat and also reduces the chance that they will be noticed. Then if a predator approaches too closer then their second response is to flee.

With our pets it’s best not to take any risks at all. If you frequently have cats in your yard ensure that when buns are out that they are within a secure pen and that you are always there to supervise. Birds of prey are also very dangerous because if you’re not always looking for them they can easily go unobserved and snatch a rabbit without any warning.

Yeah it really depends, some would fight some would run and some would freeze, you have to be careful about predators, if that cat were to attack they could have died.