wavefunction - Physical interpretation of nodes in quantum mechanics

In Schrödinger's approach to quantum mechanics, we talk about the probability of finding a particle in a definite location in space. Now if we look at a simple quantum mechanical system, say the behaviour of particle in harmonic oscillator potential, we see that there are nodes, indicating that the probability of finding the particle at those points is zero, indicating that the particle cannot be at that place. This does not make sense to me physically. So I was wandering what can be so special about that point in space that the particle cannot be there?