Spoken like someone who has not yet fathomed the infinite vastness of space (no insult intended!).
The reason it intuitively 'feels' to be improbable, is because humans are not naturally inclined or socially conditioned to think in terms of the interminable vastness - both physically and mathematically - that 'space' holds. (We could get into how space shoud really be considered to be spacetime and that there can be no real separation between the two, but that's for another time...). Our tiny minds are constrained when we try to imagine things on the terms of 'infinity'.
Mathematically, we can be almost certain that there is life on other planets; within visible space alone its been calculated that there are probably 10^18 habitable planets actually hosting some form of life, and in our galaxy alone, its probable that there are about 10 million habitable planets hosting life. And this is only on the assumption that life needs the conditions that we have on Earth in order to spark, exist and thrive; it says nothing of the interminable vastness of forms that life may actually take, outside of our current understanding of life.
Do I believe that 'aliens' are currently visiting our planet or are studying us right now? No. Do I believe its possible that they are out there? Absolutely, its almost a mathematical certainty...
Just a couple of cents...