The probability distribution over hypothesis or variable $x$, in Bayesian statistics, before seeing some batch of data.

Minimum-information prior

For positive real values: Exponential distribution

You can have improper priors that give valid posteriors.

Often flat priors

Conjugate prior

Objective prior

Priors with some objective analytical properties, like invariance to reparametrization.

Objective Priors: An Introduction for Frequentists

Jeffrey's prior

Reference prior

Rational ignorance: simpler models learn more from finite data, priors in Sloppy models

Learning Approximately Objective Priors

Carnap's theory of a priori probabilities

https://www.wikiwand.com/en/Cromwell's_rule