The title says it all. There's a point in the episode near the end where Pete meets Don in the hospital to ask about "what happened", possibly indicating that he only heard that something was wrong, but not specifically about Roger.
How exactly did he find out about this information? There's very little chance that Don contacted him. The only thing I can think of is that he went back to the office to get something and saw Bert and Joan there and questioned what they were doing.
I know the point of not revealing how he found out is to emphasize how Pete is sort of mischievous and just finds out information in sly or underhanded ways, but I need a logical reason as to how he found out.