Is there a possible reason for having index on (a) and on (a,b) at the same time Suppose I have a table with several column, among them - columns a and b.

Is there any use case for which having both multi-column index on (a,b) and a single-column index on (a) is beneficial?

AFAIU for simple equality check using first column of multi-column index is equally good as using the single-column index.
You are right. The index on (a) is not necessary if there is another one on (a,b). 

The only situation where this might (!) be helpful is, if a lot of index only scans are done on the indexes (something like select count(*) from foo where a = 42) and b is e.g. a large text column. 

The index on (a) will obviously be a lot smaller, so an index only scan on that index will be faster (whether or not that "faster" is actually measurable depends on the data in the column b)

But I would consider this is an edge case with a very specific workload.