It will always sum (or integrate) to one with respect to the data. For example, given likelihood p(x1, x2, ..., x_N|params), summing (or integrating) over all p

It will always sum (or integrate) to one with respect to the data. For example, given likelihood p(x1, x2, ..., x_N|params), summing (or integrating) over all possible values of x_1 ... x_N will indeed yield 1.