What is the probability of two sine signals producing peaks at the same time?
Let us assume that the two are independent and have the same frequency, but with different amplitudes. A peak is sure to occur for one of the phase angles in $0$ to $\pi$.
Can this be extended to 3 signals? How to find the probability density function of the sines?
If you mean at the same time exactly, the probibility is $0$. If you mean within a certain range, then the probability can be calculated using the probability density function.