Calculations and distance limitations aside, the probability of detecting extrasolar civilizations is only limited by our desire to find them. We have no idea how large the universe is. At present we only have speculation and educated guesses to guide us. For all we know there may be no end to it, the universe may be infinite. Man tends to relate all things to himself to the end of foolish narcissism. We tend to believe the universe has an end because we have an end, but this has no basis in fact. To find something in that much space you have to go and look for it, not search from one place.
Astrophysicists actually know very little about the universe. According to current research being conducted by the Supernova Research Project 70% of the universe is made up of a theoretical energy known as dark energy; this means at best 70% of our knowledge is only theoretical. Their current research also suggests the universe is expanding. This would imply there is no boarder containing it.
We are currently searching this ever growing universe though a project known as SETI. Here again our foolish narcissism may be our down fall. They are searching for extrasolar civilization by listening for radio waves. What makes us think that another life would use radio transmissions, just because we do? It seems we are not looking for any other life form, but just for ones who are like us. We may be an anomaly in the universe, an accidental creation and there is nothing else like us. We must leave open the possibility to an entirely different type of life, nothing like us.
Only looking for other civilization by listening for radio waves is like trying to find a needle in a haystack by listening for it to move. The only sure way to reduce the probability of finding other life is to go find it. Yes, at present we can not travel fast enough to cover much area, but the more effort we put toward this goal the faster we will go.
Conventional propulsion is only one method to explore and its limitation is obvious. New technologies will emerge through research and ways of travel we have not even conceived of will be discovered. To a cave man the electric light would be some sort of magic from the gods, but to us common place. This is what the future of space travel holds.
Light speed seems to be the speed limit of the universe, but that is because we have not discovered any thing faster yet. Traveling at this speed is only theoretical at this point and nobody knows what would happen if we did. Traveling at the speed of sound was at one time theoretical and thought impossible, but it is a common ability now.
The probability of finding extrasolar life will increase with the increase in technology. We cannot find something if we do not look for it. The best way to look is to go and find it. If we stay on earth to look for something far out in the universe, it is like playing hide and seek with someone in Japan when you are in New York.