事(こと)はないThere is no need to, Never happens

These forms are opposites in meaning. ひつようがある shows something must be done, as in 行く必要がある ('You need to go.'). ことはない reassures that something doesn't need to be done, as in 行くことはない ('You don't need to go.'). One expresses necessity, the other expresses lack of it.

ことはない and すこしも～ない are both emphatic negatives, but with different nuances. ことはない means 'There's no need to (A).' or 'There are no instances of (A).'. For example, 心配することはない ('There's no need to worry.'), and 彼と話すことはない ('There are no occasions when I talk to him.'). In contrast, すこしも～ない emphasizes absence of degree or amount, e.g., すこしも心配していない ('I'm not even a little bit worried.').

ことはない and なくてもいい can overlap when expressing 'There is no need to...' or 'You don't have to...' For example, 心配することはない and 心配しなくてもいい both mean 'There's no need to worry.' However, ことはない can also be used to express that something never happens. For example, 彼と話すことはない means 'I never talk to him,' which is not a use for なくてもいい.

ことはない has two primary uses: one is to express that there is no need to do something, e.g. 心配することはない ('There's no need to worry.'), and the other is to say that something simply doesn't happen, e.g. 彼と会うことはない ('There are no cases where I meet him.'). In contrast, はずがない expresses the speaker's strong denial or disbelief regarding some possibility, e.g. 負けるはずがない ('There's no way / It's highly unlikely we will lose.').