Klein-Gordon equation in quantum field theory is known to suffer from the possibility of negative probability. So, the question is, despite this, Klein-Gordon describes spin-zero field. So, how can negative probability and scalar field co-exist?
In QFT, we reinterpret the probability density as the probability charge density. In other words, negative probabilities correspond to antiparticles.
In fact, the Dirac equation which describes spin-1/2 also has this property, and it led to the prediction of the positron as the antiparticle of the electron.