Only use an upper case "P" in "professor" when it's written as part of someone's official title, not when referring to professors in general:

June Miller is the Professor of Confectionery Combat and is highly respected among the other professors in the university.

Likewise, only use upper case "F" in "fellow" when it's written as part of an official title, and not talking about fellows in general:

John Scrub is the Fellow of Alliterative Chronology. The other fellows are extremely jealous of his remarkable hair.

<aside> 👀 Never abbreviate professor to prof. See Abbreviations and acronyms for more on which words we do and don't shorten.

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