JERUSALEM, Jan 9 (Reuters) - The Omicron-adapted COVID-19 vaccine booster developed by Pfizer Inc (PFE.N) and BioNTech SE (22UAy.DE) sharply reduced hospitalizations among older patients, Israeli researchers said on Monday, in some of the first evidence of the jab's real-world effectiveness. It found an 81% reduction in hospitalizations among people aged 65 and older who had received the booster against those who had previously received at least two COVID vaccinations, but not the Omicron-adapted shot. The study was carried out from the end of September until mid-December and looked at 622,701 people aged 65 and over who were eligible for...