This is a great question, but unfortunately no one will be able to give a definitive answer as to the chances.
This is simply because we do not yet know if life exists anywhere other than Earth. It is still within the realm of possibility that Earth is the only place where any kind of life, what to speak sentient life, exists.
Finding such life would be an affront to many religions that contend that God created life on Earth only, and therefore finding even a fossil of a microbe on another celestial body would be the holy grail of science and have reverberating effects throughout human society. The theory of evolution would be proven.
It is believed to be highly likely that life does exist elsewhere in the universe simply by the laws of probability, but that being said, we have found no evidence to support this theory.
So now we can come back to your original question: “What are the chances of two planets from the same solar system having sentient species that reach space exploration around the same time?” Based on the fact that life has not been discovered anywhere, the chances to sentient life forms existing in the same solar system is practically nil (but not impossible).
Are octopuses originally from another planet? It sure seems so, doesn’t it? They are a very weird creature!
But just because they are weird doesn’t mean they’re from another planet! In reality they are related to several other Earth critters. They are a mullusc and belong to the class cephalopoda along with squids cuttlefish and nautiloids. So although they are very weird, they are definitely not from another planet.
However, in the sense that we are all made of stardust that came from some Supernova explosion somewhere in the universe, then we are all from another planet or star!
I found this movie on YouTube. It’s in black and white. I thought it would be another B rated movie about green men from Mars. It was not.
A scientist played by Peter Graves, AKA original Mission Impossible guy, establishes communication with an advanced race of beings on Mars. Communication is done with radio signals.
It turns out Jesus lives on Mars and traveled to Earth to give his Sermon on the Mount. The messages from Mars reestablished the existence of God and causes the Soviet Union to collapse and the entire world to become Christians.
We never knew Mars was so important!
The movie, in the end, came across like a Sci-Fi version of Ben-Hur.
Life exists on Planet Earth in all kinds of places that are not where you would expect life should exist. Therefore, life could exist on other planets with similar bizarre climates.
Deep under the ocean there are volcanoes erupting. The water temperature is way above boiling there and yet we have found these areas teaming with life.
Life has been found in bubbling hot tar.
The Deinococcus is listed as the “world’s toughest bacterium” in the Guinness Book of World Records because it withstands huge amounts of radiation that no life should be able to withstand.
Pitch Lake in Trinidad is 250 deep and bubbling with hydrocarbon fumes seeping from oil reserves and is full of microscopic life.
Lake Untersee in Antarctica has been iced over for 100,000 years. It is here they find Stromatolites mounds built by microorganisms.
Researchers found these autochthonous organisms at the bottom of a South African gold mine.
Credit. So if life can exist in all these unexpected places on Earth (and more) then there is some possibility life can exist in different environments on other planets. The problem? We just haven’t found anything yet.
Pretty much all of science and scientists in the world believe in extraterrestrial life, even though no evidence of extraterrestrial life has ever been found to date. Why do scientists believe in extraterrestrial life? Simply because there are billions of stars in the Milky Way galaxy and billions of galaxies in the universe. Somewhere it is highly likely that extraterrestrial life exists. It is even possible that extraterrestrial life of some form or another exists on Titan, within our own solar system!
An alien invasion by secular and militaristic extraterrestrials would solve one of the biggest problems we have here on Earth. That problem being: does life exist on other planets? Finally we would have an answer!
Planets that formed over 10 billion years ago are about 5 billion light years from us, meaning that if we could somehow study planets that far away (we can’t) the light reaching us from there would have taken 5 billion years to reach us. Therefore, we’d be seeing what the planet looked like 5 billion years ago, not what it looks like now. Below is what we are able to see of the most distant galaxy that we have seen to date. It’s about 13 billion light years and we are just seeing the early stages of development because it took light 13 billion years to reach us.
As you can see from the image, Hubble can barely make out the galaxy, what to speak of any planets that might be orbiting the billions of stars inside that galaxy. The best we can do is study planets in our vicinity of the Milky Way.
First, we don’t know Earth is the only habitable planet. However, until we have some proof, we have no way of knowing for sure. That’s why we’re searching so hard for extraterrestrial organisms.
Second, who says the universe has to have a use? It just is. Similarly, you could say what’s the use of living if you die in the end. That kind of view doesn’t do anyone any good. Just go with it and enjoy the exploration and discovery life offers us, like whether or not life exists elsewhere in the Universe.