Why is 在 used in this sentence?
Why is there 在 "她喜欢在喝酒后抽烟。"?
In this case, the 在 expresses the "when" of "smoking" and is a set with 后 to mean after; it does not express present progressive but rather sets up the circumstance under which "She likes to smoke".
"在......后": after (doing) ___
"在喝酒(之)后": after drinking
"她喜欢在喝酒后抽烟。": She likes to smoke after drinking/She likes to smoke after she drinks.