Since the data is replicated thrice in HDFS, does it mean that any calculation done on one node will also be replicated on the other two?

Since there are 3 nodes, when we send the MapReduce programs, calculations will be done only on the original data. The master node will know which node exactly has that particular data. In case, if one of the nodes is not responding, it is assumed to be failed. Only then, the required calculation will be done on the second replica.