PROOF of space aliens:No $#!t, the footprint below was made on the moon by a creature from another world!
But seriously, there is a problem with the mathematical likelihood assumption. This idea assumes that because space is vast and full of worlds not to different than ours, there is a good chance that other life exists. And just as we predicted that we would find other planets it is predicted that we will eventually find other life.
That makes sense, but the problem is that we have only one example of life. If we had even two examples then we could assume that life is common in the universe. One data point tells you almost nothing. Since all living things we are aware of are actually the same one living thing and species are just variations of that first DNA life form, it is possible that life only happened once and this is it.
It's true that it could be the case that some step required for the appearance of life is so unlikely, that it only ever occurred once - after all, we still don't even understand all the steps that lead to it. But if it happened once, then we know for a fact that no matter how unlikely, it is possible. All other things being equal, if we have very similar values for all of the variables that led to life on Earth, we would probably get a similar outcome.
And indeed, as you say, space is vast, the number of worlds not too dissimilar to Earth is probably large, and the chemical elements that we know are required for life similar to ours is abundant throughout the universe. But there are at least 3 other things you also have to consider:
One, the possibility that life as we know it is not the only way life can exist - sure, we only know about one type, but I know of no reason why it should be unique. Perhaps life can be composed of (slightly, or not so slightly) different elements than those that life on Earth is based on, increasing the chances for it appearing elsewhere.
Two, even if life as it exists on Earth is the only way life can exist, it could still be the case that it originated elsewhere first, and somehow found its way to Earth - and perhaps other welcoming planets as well. Or perhaps some more elaborate components that it requires did: water (
http://www.iflscience.com/space/solar-systems-water-predates-sun), "biologically interesting molecules" (
http://www.space.com/1686-life-building-blocks-abundant-space.html) and so on could be sufficiently abundant to kick start the process in several places at once.
Third, time. Often forgotten, but the universe is over 13 billion years old, and it could be that the conditions for life similar to that on Earth to appear have existed for some 8 or 9 billion years - ~ since stars similar to the Sun started coming along (population I stars). That's plenty of time for unlikely events to occur repeatedly. And perhaps one reason for why we don't see any evidence of intelligent life out there at the moment is that we are just too young and primitive, and most others are a couple billion years older - who knows, we may not even be able to recognize them for what they are if we got a change to see them.
These people would have investigated all the available data before doing the life-hunting on Mars project -
http://www.space.com/27073-exolance-mars-life-search-idea.html .
This means that as far as anybody knows, there isn't any life out there. Anything to the opposite is simply speculation. My one fear is that we are going to inadvertently introduce life out there, and then we'll try to claim we found it.
Of course, this project might be a great way to covertly start terra-forming Mars.
Even if it was the case that life was introduced elsewhere from Earth, the similarities would likely make it obvious there was some sort of relationship - that is, we'd probably have a good idea that it either evolved from a previously known organism, or lacking that, we could at the very least suppose there was some prior common origin to both sources of life.