Question

Suppose that a qubit is in the state |\phi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle where a\in[-1,1]. If we first perform a standard basis measurement on this qubit and then perform a |u\rangle,|u^\perp\rangle-basis measurement where |u\rangle=b|0\rangle+\sqrt{1-b^2}|1\rangle for some b\in[-1,1], what is the probability that the outcome of the second measurement is u, in terms of a and b?

Explicitly indicate multiplication with a * symbol.