In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure. The PCA is merely a mathematical manipulation to recast m variables as m factors. Factor analysis (FA), however, brings a priori knowledge to the problem solving exercise.

'There is a short list of primary assumptions behind factor analysis. But basically. factor analysis assumes that there are  cowelations/covariances between the m variables in the datp set that are a result of p underlying, mutually uncorrelated factors.