Test services presented in attached file. Their ids: Test - serviceid=1, Test2 - serviceid=2

Parameters, used in API request:

{
  'serviceids': serviceid,
  'intervals':[{'from':tPrev.strftime('%s'),'to':tNow.strftime('%s')}]
}

Result with serviceid=1:

{u'status': u'4', u'problems': [], u'sla': [{u'from': u'1435487809', u'problemTime': 30, u'to': u'1435487839', u'okTime': 0, u'downtimeTime': 0, u'sla': 0}]}

Result with serviceid=1:

{u'status': u'4', u'problems': {u'3038': {u'triggerid': u'3038'}}, u'sla': [{u'from': u'1435487898', u'problemTime': 30, u'to': u'1435487928', u'okTime': 0, u'downtimeTime': 0, u'sla': 0}]}

At first, documentation does not specify, that array 'problems' is only for services, linked to triggers directly.
Then, WUI shows triggers, caused problems via services tree.

So, current ticket (case) is marked as 'Bug related to API(A).
And I'm not sure about Priority.

Used doc: https://www.zabbix.com/documentation/2.2/manual/api/reference/service/getsla