In the PostgreSQL, You can also calculate RANK of a query using available windows functions.
Like SQL Server, PostgreSQL also provides functions like: RANK(), DENSE_RANK().

I am sharing one demonstration on calculating RANK of students bases on their marks. I require top 3 students result where more than one student has same marks.

Create a table with sample data:

CREATE TABLE tbl_Students
(
	StudID INT
	,StudName CHARACTER VARYING
	,TotalMark INT
);

INSERT INTO tbl_Students 
VALUES 
(1,'Anvesh',88),(2,'Neevan',78)
,(3,'Roy',90),(4,'Mahi',88)
,(5,'Maria',81),(6,'Jenny',90);

Using DENSE_RANK(), Calculate RANK of students:

;WITH cteStud AS
(
	SELECT 
		StudName
		,Totalmark
		,DENSE_RANK() OVER (ORDER BY TotalMark DESC) AS StudRank
	FROM tbl_Students
)
SELECT 
	StudName
	,Totalmark
	,StudRank
FROM cteStud 
WHERE StudRank <= 3;

The Result:

studname | totalmark | studrank
----------+-----------+----------
 Roy      |        90 |        1
 Jenny    |        90 |        1
 Anvesh   |        88 |        2
 Mahi     |        88 |        2
 Maria    |        81 |        3
(5 rows)