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).