Chance are negligible. If collision occurs with a funded address, attacker you can transfer funds elsewhere.
Chances are still negligible when 1 billion people are using it? also can't I just run some kind of bots, that randomly generate addresses to see if
they have funds in them?
Yes, chances remain negligible. You could run your bot, but it'd be a waste of electricity. Chances are you'd wait the lifetime of the universe before finding a collision.
But probability also says, I could have a success on my first run? isn't it?
Sure, you could absolutely find a success on your first run, but let's apply probability to your scenario.
Let's say there are a billion people using 10 addresses each for 10 billion total addresses.
This means that each address you generate has a (1/2^160)*10,000,000,000 possibility of holding a balance, giving your first attempt a 0.0000000000000000000000000000000000000684% chance of finding a collision on your first attempt.
You are correct in stating that with each try it will either happen or it won't, there is no in-between state, and you're correct in stating that it's possible. It's also bad news for the account holder that a collision would give you control of those funds.
Comparatively speaking, your odds of being struck by lightning in a given calendar year are about 1 in 280,000. The odds of winning my local lottery are about 1 in 176,000,000. So finding a collision on your first try is roughly equivalent to being hit by lightning 16,540,000,000,000,000,000,000,000 times per second for an entire year or winning the lottery 830,000,000,000,000,000,000,000,000,000 times.
If you find a collision I would stay indoors and play the lottery.