It's an interesting thought experiment, but not too meaningful. The universe is still young; it's been around for 13 billion years, the Earth for 6. Given the immense distances involved, and the complexity and resources required for interstellar travel, it's not surprising we wouldn't have seen life.
And, for a moment, let's suppose your thought experiment is true, and there's an alien probe somewhere in our solar system. Would you be surprised we haven't found it yet? There're an awful lot of places left to look.
1. I was wondering if we could apply an anthropic type of argument here? We are having this argument at this time and place because we predate the colonization by self-replicating bots / other end-of-world scenarios. Multiverse version: any time we're having this discussion, we are on the surviving branch predating self-replicating bot colonization that renders the planet unlivable. I realize this type of argument can be extended to reach absurd conclusions, but nonetheless it's an entertaining thought.
2. What is life? What is civilization? What are their goals? Why do we assume a society of relatively independent individuals? Is it even a sustainable model for a post-human level civilization? Aren't we anthropomorphizing aliens a bit too much? What if a civilization either dies out at human-level stage or necessarily reaches a mental unification point and all its further activity is inward focused? I think we're on the first stages of self-awareness compared to rocks and jellyfish, imagine the level of self-awareness experienced by a far more advanced civilization. Would it necessarily be resource and space-greedy and try to colonize the galaxy? At least it's not immediately obvious to me why it would.
3. Another point is, what scales are we looking for? Doesn't our scale essentially depend on the planet / star system we evolved in, and the scale at which original life started? What basic building blocks / resources does alien life use? Maybe they rely on physical resources we haven't yet explored (dark matter, etc). Essentially I'm agreeing with the people saying "we don't know what we're looking for".
I really liked point 2. It seems to be the default assumption that we as a species should seek to increase our chances of survival by looking to colonize other planets. However it is entirely possible that our mindset may change in the future and we come to the conclusion that, even with capable technology, it is better for us to live out our existence on this planet.
"Assuming the above is true, then why do we not see any sign of these probes?" Because for example these probes are as tiny as a nano-meter? Hey it is the year 2012 here on earth. In the last decades we have already shrunk computers from the size of a entire room to fit in our pockets and soon our blood. And we ourselves can already build nano-technology, despite not being able to travel around our galaxy. What tells us that intelligent life has to build "probes" so big that we are able to detect them. Maybe these probes are just as large a nanometer and are already flying towards us or were near us or are already on Pluto. Or maybe other life forms shrink themselves to fit into a trillionth of a trillionth of the diameter large spaceship to be able to travel around space faster than light. All of the theories are just expanding from current knowledge as of today, not factoring in any stunning surprises of how the universe might really work :)
This seems like a good point on the surface, but since it takes only one outlier to dominate the universe (by Bostrom's train of thought), then it would have happened anyway. It's the law of smart for one, dumb for all. Assuming most life forms would decide to live minified, any life form not deciding so would have immense advantage to consume all untapped resources. Following this logic, and since any sufficiently advanced replicators would all be competing for the same space, the most overwhelming kind would take over all others.
Suppose that we start near the edge with a self-replicating probe that can spread outwards no faster than Voyager 1. In 2 billion years, every solar system in the Milky Way would be chock full of factories trying to expand.
And there is no need to assume that it is so slow. We have already designed technologies to send probes to stars much, much faster than Voyager 1. Here is one. Put a bunch of solar panels on Mercury, and use the power to shine a laser into space. That can push on a light sail, pushing the probe outwards at something like 1% of the speed of light. Then as it nears its star, let the sail fly away, shine the laser again, and have its reflected light brake the probe.
With this level of technology, which may be feasible for us in just a few hundred years, the colonization of an entire galaxy can be reduced to tens of millions of years.
If technological life is out there in our galaxy, in the blink of cosmic time finding evidence of it will not be a search for a needle in a haystack - it will be closer to finding a piece of straw in a haystack.
And, for a moment, let's suppose your thought experiment is true, and there's an alien probe somewhere in our solar system. Would you be surprised we haven't found it yet? There're an awful lot of places left to look.