Well, He's been a top suspect for many years. You can read The Cases that Haunt Us by John Douglas, a former FBI profiler who goes through the case and explains why he thinks the evidence leads to Kosminski. What he has to say is pretty compelling. That said, there are a lot of holes in the recent DNA analysis-- we don't have the records, we haven't seen what the lab did, the lab didn't use a double-blind study. There's about a zillion ways the shawl could have been contaminated between the murder and now. So while there is a compelling case for Kosminski, there is still doubt there. I can't give you any numerical value to the chance he's the murderer, though. There's nothing that clearly outrules it. It's just that the evidence is tenuous.

My information may be a bit dated as it's been about a decade since paid much attention to the Ripper killings. At that time at least the late Phillip Sugden was the most scholarly authority on the killings. He devotes a chapter to Kosminski in The Complete History of Jack the Ripper. He found many flaws to Kosminski being the Ripper. To me the most compelling was that if Kosminski was the Ripper he would have killed five or six women over the course of a few months and then stopped killing for a couple of years prior to being put in an asylum. Even adding in the non-canonical killings that still makes it unlikely, in my mind at least, that Kosminski could just stop killing for any length of time. Also, he was in asylums for over two decades. In the surviving records there is very little indication that he was thought of violent or dangerous. Sugden goes into the eyewitness accounts the Ripper and points out how they don't match Kosminski too.

What about the surgical knowledge? Isn't Jack the Ripper supposed to have some surgical knowledge on the organs and such? How does Kosminski match this?

What about the letters ? Don't they show a typically British handwriting ?