This is very poor wording on your part. "Bahavior" is arbitrary, or is governed by rules, and is never random. Hence, there is no such thing as "random behavior." It is a contradiction in terms.
Otherwise, Darwin's theory of evolution is based entirely on random occurrence of events.
Examples involving engineered things are inherently invalid and don't work. Evolution is like shaking up a solution of many substances and the heavier substances settling to the bottom, the lightest substances floating to the top, liquids separating based on density, etc.
I believe you mean a hypothetical evolution of eyes since no one knows how eyes evolved, or if Darwin's theory is even correct.
Correct. All acceptable proposals for how eyes might have evolved per Darwin's theory of evolution involve very small changes over long time periods.
It's better to say that it is simply entirely random. The moment you claim a "probability," you put yourself on the hook to explain both what that probability is and how you computed it.
Correct ... according to Darwin's theory. If some Christians are correct, everything happened a few thousand years ago, and I'm going to have some explaining to do when I get called into Peter's office.
Well, it has the advantage of working over a long but unknown period of time. It could be millions of years. It could be billions of years. Nobody knows.