Chances that we find extra terrestrial life is possible, yet it may not necessarily be what we want. Even if we find bacteria on another planet anywhere that classifies as extra terrestrial life. However, I think most people think of little green men when we talk about extra terrestrial life, and that I am not so sure about. It could be, but there is a higher chance for something more simple.
Why shouldn't there be alien life in outer space? Once we space travel more often, we are bound to bump into another species of aliens. The probabilities that aliens exist is over the top considering the vastness of our universe. It is sort of arrogant to claim that our Earth is the only one with life in the universe. It is like a country who has never traveled far into sea, sees nothing in the horizon, and then claim that that is the only country with intelligent life prospering.
First of all to find them, they have to exist in the first place and there is no evidence to suggest we aren't the only ones. Life has only proven to exist on one place - Earth.
Secondly, if it does then it is likely to be extremely rare and on worlds hospitable for life to grow. Most other worldly bodies are gas giants like stars, pulsars, neutron stars, and gas planets. Even when there are solid massed planets and moons they are usually either too cold or too hot for life to live and prosper. Then, even under the right conditions and circumstances you need to hope the 'soup' of life even happens and goes anywhere.
Which brings me to the third point. If life does exist it's very likely it would be in the form of microbes. Even then, if were to be more than that what chances are that an extraterrestrial lifeform would grow sophisticated, intelligent, and technologically gifted enough to actually attempt to seek us out? It's only happened once on Earth, and our story as a species is quite honestly a freak of nature.
Finally, the range of distances. We haven't even travelled much further than the outer space of our solar system (even then it's in the limited capabilities in form of probes). We haven't even landed a single man on our neighbour mars let alone a planet in another solar system, or even another galaxy which the nearest would be 2.5 million light years away. Too far, for todays and tomorrows technology. This is not something than even aliens can easily over hurdle even if they are more technology advanced than us. Our signals billowing outer space have so far picked up nothing in return. It's our greatest hope of contact and it hasn't been a success. I doubt it would ever be.
The universe is 13.8 Billion years old. Earth is only 4.5 Billion years old. That leaves 9.3 Billion years prior to Earths formation and humans have only existed in our most primitive form for only about 50,000 years. That leaves a lot of time for something else to evolve elsewhere, perhaps before or faster than us. I hope we find it first, but I am doubtful.