Adjectives licensing to-infinitival

Meaning	Examples
Disposition / willingness	eager to help, reluctant to leave, willing to cooperate
Readiness / imminence	ready to begin, about to leave
Likelihood / certainty	likely to win, certain to fail, sure to notice
Ability / suitability	able to swim, fit to work
Evaluation / difficulty	easy to understand, difficult to justify, pleasant to read
Emotion / reaction	happy to help, sorry to hear that, surprised to discover it

The important point is that they do not form one uniform semantic class. What they share is mainly syntactic: the adjective licenses a to-infinitival complement.

They also differ syntactically:

Emma is eager [to leave].

Emma is likely [to leave].

This book is easy [to read].

Example	Construction	Relation
Emma is eager [to leave].	Subject control	Emma is an argument of eager and understood as the subject of leave.
Emma is likely [to leave].	Subject raising	Emma is semantically selected only by leave, not by likely.
This book is easy [to read].	Hollow-clause / tough construction	this book is an argument of read, corresponding to its missing object: read this book.

Emma is eager (independently meaningful, Emma controls [to leave])

Emma is likely (likelihood applies to [Emma leaves])

This book is easy → more precisely, [to read this book] is easy

Note

Eager semantically selects a person/experiencer, whereas likely does not.

The difference between control and raising is the lexical licensing: That is why the first is control and the second raising.

A useful diagnostic is dummy subjects:

There is likely to be a problem.

There is eager to be a problem.