Here’s an evolutionist’s dream: 10,000 planet Earths, starting from the same point at the same time, and left to their own devices for four and a half billion years. What would happen? Could you go on safari from one planet to the next seeing an endless procession of wildly different organisms? Or would many of the planets be home to life forms that are broadly similar?
This is the sort of question that's hard to answer a priori. Basically, evolution is made up of a ridiculously large numer of random decisions, each with a very small effect. There are a lot of classes of combinatorial structures for which we can generate members of the class uniformly at random (or according to some other probability distribution; the details don't matter here) and they'll all basically look the same. Why shouldn't evolution be like that? The details will be different every time; but in broad outline one can imagine that a "law of large numbers" and "central limit theorem" could apply to evolution -- if we consider some numerical measure of some evolutionary trait, then if we average that numerical measure over many independent "runs" of evolution we should approach some limit, and the deviations from that average might even be spread out according to a normal distribution.
Of course, this isn't something that has to be true -- the many events that make up a single evolutionary process aren't exactly independent, some of them can only happen if others happen, and so on. And whatever numerical measure I was talking about in the previous paragraph might only exist in some runs and not in others. That would seem to argue against my hypothesis. But on the other hand, evolution isn't just a random walk. There are selection pressures which are the more standard explanation for what's known as "convergent evolution", which is the indepedent evolution of similar traits in evolutionarily distinct populations.
By the way, on the topic of convergent evolution: the eye has evolved something like forty times. This suggests that eyes are very likely to arise via the evolutionary process; things that have only evolved once among all life, like language (although that's open for debate), are given the state of our current knowledge less likely to arise. One might be able to compute something like the "probability" that eyes, language, or some other complex trait evolves by looking at how many times it has arisen independently. But this is the sort of probability that is very hard to interpret -- what would it mean to let evolution happen more than once?