With vastness comes separation. The more vast it is the more likely there is life elsewhere, and the less likely its in travel rangeor would be able to identify life on earth.

I’m sure you’re aware, but this is known as the Fermi Paradox (for people who want to do more reading).

Very very big and very very old. Take the probability of an intelligent being evolving, multiply that by the probability of it being on a planet that had vast amounts of practically free energy stored from the last great extinction and figured out how to use it, multiply that by the probability of them not running out of that energy until they can develop new sources (without destroying each other in the process), then multiply that by the probability of them figuring out space travel, multiply that by the probability that they are within reach of us with that technology, multiply that by the probability that they care enough to come over here, and finally multiply that by the probability that this occurs within the 2000 years or so when we aren't too ignorant to appreciate it.

We’ve addressed this before. It’s the Fermi equation

The possible shapes of life are much bigger than the universe.

The chances of intelligent life existing outside Earth are lower than the chance of that same intelligent life speaking flawless Swedish. We might as well send some Europop records to space as signals to aliens.

"Intelligence" is a human invention created by humans to describe humanity. It only applies to humans and human-like beings.

Intelligent life might happen on every 10,000th planet or it might only happen in every 10,000th universe.

As long as we know of only one occurrence of intelligent life we have no clue of the probability. And human intuition on what's right doesn't help us here.

We still have only one data point for life and one data point for intelligence.

It's absurd to claim intelligent life doesn't exist, as we know it does on Earth. And it's absurd to claim any level of probability for other intelligent life until we have one more data point.