What is most likely to happen(in a series-connected string of holiday ornament bulbs) if one bulb gets shorted out?

When one bulb is shorted out in the holiday string, the connection will continue. However, as one bulb is gone there is one less resistance. This means as the resistance goes down and the voltage is constant, the current will go up. This is by law of physics and the equations connecting the values of current voltage and resistance.

All of the three values are interlinked. When one value changes or drops, the pothers change as well. In this particular constant, the voltage is kept constant. Hence, the current and the resistance and changing. Here the resistance went down and automatically, the current went back up.