The probability of finding a civilization within a century of our development is extremely small. A model most favorable to civilizations close to us in development might constrain the period in which such civilization could arise to 200 million years. Dealing only with our galaxy for the moment, such a model might stipulate a million civilizations with radio technology.
Assuming an even distribution of these civilizations across the 200 million year time span, there would be only one civilization within three centuries of our development—us and one other. There would be only five within a thousand years. To put it in other terms, 99.9995% of the civi-lization would be more than one thousand years ahead of us.
If the time span in which radio technology civilizations could arise were greater than 200 million years, or, if the number of civilizations were less than a million (both of which seem very likely), the number of such civilizations would fall. At a billion years and a thousand civilizations, for instance, 100% of the civilization would be more than one million years ahead of us.
One way around this would be to constrain the life span of a technological civilization. But such an effort would produce the effect of reducing the number of such civilizations existing at any given point in time. I don't think such an adjustment is relevant to this analysis, since it wouldn't change the number of civilizations that are no more advanced than us.
In the next decade we may begin analyzing the atmospheric gases of extra-solar terrestrial type planets within 50 light years or so of Earth. By looking for water vapor and ozone we will get some very good ideas of the existence of life on these planets. Imagine what we’ll be capable of in a 100 years, let alone a thousand: detection of freon, direct imaging of the planets, uses of lead, isotopic and other analyses to determine energy sources, agricultural activity and industrial processes, and lots of things I haven’t thought of, and probably many things nobody has thought of yet.
To put it another way, doesn’t it seem very likely that nearly all of these 1000 advanced civilizations in the galaxy will know there is life here on Earth? And life using photosynthesis? A signal that's been broadcast from Earth for two billion years. Depending on how close they are, they will know something about the agricultural revolution, metal working, the industrial revolution, the use of refrigerants and nuclear processes, and, perhaps, a lot more. As well as radio and television. If super-luminal communication is possible, it won’t matter how close they are.
When we, for the first time, discover an extra-solar planet with photosynthesis, doesn’t it seem awfully likely that we will study that planet very closely for a very extended period of time? And, a few centuries from now, what about a flyby? An orbiter? A lander? Think of how advanced computers will be by then; and the software, even the hardware, can be continuously up-dated to take advantage of technological advances on the way, albeit with an increasing delay.
If we will be able to do this analysis and initiate this type of mission, doesn’t it seem likely that at least some of these advanced civilizations would do similar things?