It's undoubtedly just coincidence, but Sen. Joseph R. Biden Jr. (D-Del.) and Patrick Caddell, the Democratic pollster and campaign consultant, were both vacationing at St. Thomas last week. Caddell, political insiders will recall, tried unsuccessfully to persuade Biden to run for the Democratic presidential nomination in 1984. But who keeps track of those things? Or that Biden has been talking to John Marttila, the Boston media guru?

Caddell, Bob Shrum and David Doak, who used to be partners, are still working for Robert P. Casey, the former Pennsylvania auditor general who is running for governor, and for Sen. Alan Cranston (D-Calif.). Shrum and Doak acrimoniously split up their partnership with Caddell just before Christmas, but they agreed to continue working together on campaigns they had started. That agreement is beginning to fray. Shrum and Doak have dropped out of Florida legislator Steve Pacjic's campaign for the Democratic gubernatorial nomination; Caddell is still in it.

Casey, who has run unsuccessfully for governor three times and is hoping the fourth time is a charm, announced last week that he is entering the May 20 Democratic gubernatorial primary. A major rival, former Philadelphia district attorney Edward G. Rendell, has been endorsed by Philadelphia Mayor Wilson Goode; moreover, Pittsburgh Mayor Richard Caliguiri has indicated that he is leaning toward Rendell, who raised $506,000 last year compared to $347,000 for Casey. For his part, Casey is expected to be endorsed by the state Democratic committee and the state AFL-CIO.