We use 'can' to talk about both ability and possibility.
'I can speak French'. (ability) 'Your computer can be customized according to your needs,' (possibility)
'Can' has no infinitive or present perfect form so we use 'to be able to'
'May' and 'might' are used either to speculate about the present or to suggest a small possibility of something.
'Jane hasn't come to work today. She may/might be ill' (speculation)
'It may/might rain this afternoon.' (there is a small possibility it will rain) Some people say 'might' suggests a smaller possibility than 'may', but there is very little difference.
Can = it is possible 'They can still win the championship!'
May/might = there is a small possibility. 'They might still win championship!'
Can and may are also used in speech to ask for permission. 'Can i borrow your pen, please?' 'May I borrow your pen, please?' Some people think 'may' is rather formal in this sense.