It's still quite unlikely. The original biochemistry needed a liquid aqueous environment to form and replicate, and you won't find that condition outside of a

It's still quite unlikely. The original biochemistry needed a liquid aqueous environment to form and replicate, and you won't find that condition outside of a reasonably deep gravity well in a solar habitable zone. Only Venus, Earth, and Mars would be plausible candidates inside the Solar System for an early incubator of life, and relatively speaking, there wasn't all that much matter transferred between these bodies. Early life probably wasn't as tough as modern bacteria, and likely used something less robust than DNA. The problem with the idea that life could have originated from outside the solar system is that Earth has a laughably small "absorption cross-section" with respect to matter ejected from another solar system, plus the fact that it's very unlikely any information-bearing polymer could survive the integrated radiation flux over its long subrelativistic journey between the stars.