Electric fence is the most cost effective way to secure a large area. They aren't fool proof - but they are highly effective. Do read the links posted above by
@centrarchid .
While many of the larger predators are dusk to dawn hunters, they are also a threat during the day - particularly in suburban areas that have encroached into rural / wilderness areas. Predators sole goal is to take in the most calories as possible, with the lowest caloric burn - they learn to go for he easiest meal. But they also learn to avoid risk and / injury. Bears, wolves, Mt Lions and packs of coyotes could easily kill most any dog - but not without risk of injury and alerting others. So it's rare that you hear of it happening.
Electric fences are psychological barriers - not physical barriers. In order to work, the predator needs to learn pain (and in some cases, the animal within the fence needs to learn the same.
I know nothing about peafowl - so can't really help with how to keep them in - hopefully someone else will jump in. But I am in a constant battle with black bear - not for my chickens, but for my beehives. In order for me to win this battle - I needed to train the bear to touch the fence. I use bacon, some use peanut butter. The goal is to get the bear to touch the fence with his nose, lips or tongue. Bear are very smart - smart enough to know to avoid the pain once inflicted. It also worked on my own dogs - who couldn't resist the bacon either. I imagine it wold work on other dogs too- but as I have no neighbors, it's not been a problem.
We don't have Mt Lion, so no advice there. We do have bobcat - and I do know that a neighboring farm lost chickens to a cat that learned to jump their fence during broad daylight. Maybe someone has an idea about how to ward off big cats.
If you have any pictures of your coop and run area, someone with more technical skills than I will likely offer very specific ideas on how to best guard your flocks.
Good luck.