1. I might go shopping later today.
2. I may go shopping later today.
Does the use of 'might' in the first sentence instead of 'may' in the second sentence indicate that there is less likelihood of my going shopping today?
In its strict epistemic meaning, 'might does denote a lesser chance than 'may', Ms Tan.
That said, modals can be used in a personal, emotive fashion so there's no way for us to absolutely discern that the speaker really means what 'might' actually denotes.
It's possible that the person is joking or lying, that they are really a shopaholic.
A: I might go shopping today.
B: Oh yeah right. 'might', hah; if you miss shopping today, it'll be because you've passed on.