In this case, the non-clustered index is essentially a duplicate of the primary key*. It will take up extra space and make inserts/updates/deletes slower, but it will not add any benefit.
The reason is that any query that can be answered by seeking on column a can perform that seek on the primary key and has no need for the non-clustered index.
However, if your actual table has many additional columns beyond a, b, and c (e.g., let's say there are 100 other columns as well), it's possible that the non-clustered index could improve queries that use only a, b, and c. In that case, it would provide a smaller data structure that can be used to access only these three columns. It would depend on your workload whether this is worth the cost of maintaining the index.
* The primary key is the clustered index here and, as Max Vernon points out, the clustered index is the table. So another way of putting it is that your non-clustered index is duplicating the whole table.
