Why does my servo execute an action in the beginning when the odds are almost 0?
Recognise that, despite the name, random() does not produce a truly random number. Because a computer is basically determinate, every time random() is called it produces results in a fixed sequence - it is possible that this sequence includes 0 or 1 straight away.

If you want it to start at a different point, you need to "seed" the random number generator by calling randomSeed() and passing in an integer. Note that it can't be the same integer every time - that would just move the sequence to the same point every time. The Arduino reference for random() suggests reading an unconnected analog input with analogRead() (which would produce different numbers at different instances in time) to "seed" the random number generator with a new starting position.

randomSeed(analogRead(A0)); // Seed random() with random starting point