What you need is to know how to use ISBLANK and IF function in formula editor. What I have done is created three fields of datatype picklist. Then, first I have checked whether any of the picklists is blank or not using If condition.
IF( ( ISBLANK(TEXT(sa_nket__Pick_1__c)) || ISBLANK(TEXT(sa_nket__Pick_2__c)) || ISBLANK(TEXT(sa_nket__Pick_3__c)), value if true, value if false )
then defined the value for true condition and false condition. Since you have another condition to check whether a particular value is selected in first picklist field, So you have to again check the condition as follows for both condition i.e value if true, value if false in first if condition:-
IF( ISPICKVAL(sa_nket__Pick_1__c , "Test 1") , TEXT( sa_nket__Pick_1__c ) , '') --> for value if true
IF( ISPICKVAL(sa_nket__Pick_1__c , "Test 1") , TEXT( sa_nket__Pick_1__c )+'_', '') ---> if value if false
Then finally merged all according to your condition as follows:-
IF(
( ISBLANK(TEXT(sa_nket__Pick_1__c)) || ISBLANK(TEXT(sa_nket__Pick_2__c)) || ISBLANK(TEXT(sa_nket__Pick_3__c)) ),
IF( ISPICKVAL(sa_nket__Pick_1__c , "Test 1") , TEXT( sa_nket__Pick_1__c ) , '') + TEXT( sa_nket__Pick_2__c ) + TEXT( sa_nket__Pick_3__c ),
IF( ISPICKVAL(sa_nket__Pick_1__c , "Test 1") , TEXT( sa_nket__Pick_1__c )+'_', '') , + '_' + TEXT( sa_nket__Pick_2__c ) + '_' + TEXT( sa_nket__Pick_3__c )
)