If we take a look at our own solar system and count the currently defined planets; Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune we know of life on 1 in 8 planets. Let's assume this is actually a high percentage and that 1 in 100 planets has some sort of life.
A septillion is 1,000,000,000,000,000,000,000,000 so that gives us 10,000,000,000,000,000,000,000 worlds with at least single cellular life. That's 10 sextillion worlds.
Ok, so let's assume 1 out of every thousand worlds has multi-cellular life. That's 1,000,000,000,000,000,000 worlds, 1 quintillion.
Now let's assume out of those 1 quintillion muti-cellular worlds that 1 in 1000 has something resembling animals. 1,000,000,000,000,000. That's 1 quadrillion worlds with animal life.
Let's assume 1 in 10 of those have some sort of sentient life that has developed the use of tools, even if they are primitive. That's 10 TRILLION worlds.
10 trillion worlds scattered among 100 billion galaxies gives an average of 100 tool-building worlds in your galaxy. Then you have 13.8 billion years to spread those out over.
With such a conservative estimate, it is highly unlikely that we will ever encounter a sentient species that originated on another planet.
We could easily change those numbers in our favor though. Say 1 in 2 stars has a planet or moon that supports life. 500,000,000,000,000,000,000,000 planets with life. Say 1 in 2 of those has tool building life, 250,000,000,000,000,000,000,000.
250 septillion planets with tool-building life. That gives you an average of 25,000 tool-building worlds per galaxy. That's still only a 1 in 20 million shot that any given star in our own galaxy hosts a planet/moon with a tool-building race on it. Then factor in that the Milky Way is estimated at 13.21 billion years old, consider humans are only about 200,000 years old and that civilization only goes back 10,000-25,000 years old (if you believe that the Bosnian 'pyramid' is a human creation then 25,000 years) and that we didn't land on the Moon until July 20, 1969, and it is the farthest we've ever sent human beings...
Now let's assume that in the first billion years of our galaxy, there were ZERO tool-building species. That leaves you with 12.21 billion years to divide 25,000 civilizations over a galaxy with 100,000-180,000 light-year diameter. Let's assume 140,000 light-years. That's more than 15,000,000,000 square light-years.
That gives us 1 tool-building civilization per 600,000 square light-years spread out over 12 billion years.
It sucks. I want to meet an off-world species sooooo much, better I want to travel to some of their worlds and see them with my own eyes. But, unless we figure out immortality I won't be holding my breath.
And obviously, this figure could be way lower than in reality. If a species develops space technology it could easily begin to spread. Even if a civilization needed a thousand years to spread to a neighboring star in 10,000 years you could have a presence in 512 star systems, in 20,000 years 524,288 star systems.