Former = the one before or one from the past e.g. the former president
prior = This word is formal. It means before, existing or happening before something else, or before a particular time: e.g. The course required no prior knowledge of Spanish. = No knowledge of Spanish beforehand :-)
preceding = existing or happening before someone or something, e.g. In conclusion, I hope the preceding arguments have convinced you of the need for action. This word is also formal.
Hope that helps!