That's very simple: if we don't end up hitting a light the path won't carry any radiance, so it won't contribute to the final image. If we start on a light and we don't end up hitting the camera the path won't carry any importance and so it won't contribute to the final image either.
Keep in mind that there is a very mathematical foundation to all this, we're not just tracing paths for the fun of it. Basically what we want to solve is a path integral (an integral over all paths), we do this using a technique called Monte Carlo integration (which basically means we use randomness). We first sample a path (using path tracing) and then we calculate the contribution of that path (which basically is the amount of radiance is carries divided by the probability of sampling the path) and then we add that contribution to the right pixel.
Keep in mind that there is a very mathematical foundation to all this, we're not just tracing paths for the fun of it. Basically what we want to solve is a path integral (an integral over all paths), we do this using a technique called Monte Carlo integration (which basically means we use randomness). We first sample a path (using path tracing) and then we calculate the contribution of that path (which basically is the amount of radiance is carries divided by the probability of sampling the path) and then we add that contribution to the right pixel.