The determination of likelihood of advancements in any science or technology over a decade are dependent upon several technical features of culture. Not all are technical because they are elements in hardware and software design. Some are.
- Market forces
- Perpetuation of traditions in education
- Availability of resources
- Cost of research
- Cost of deployment and sustenance
- Natural cultural balance of curiosity and fear
The low level cybernetic conversations with service applications like Siri and Cortana were correctly identified in the question, and Google Assistant should be included. If a survey is done of these conversations by working around public relations, perhaps by using a competitor search engine to locate PR unfriendly records of conversations, the low level becomes immediately apparent1. Anyone could confirm this by asking these service applications a set of the popular questions in a set of the StackExchange sites. Most if not all of them would produce answers that would be down voted if not deleted.2
These service applications are efforts to meet the criteria of Alan Turing's thought experiment, which Turing called The Immitation Game3.
How high levels is it going to reach (likely) in future years?
Prediction of AI milestones is not possible without defining first the milestone criteria to be met. Let's pick seven coveted ones.
- A service application the answers of which can gain StackExchange reputation faster than humans, which is a more demanding version of Alan Turing's thought experiment
- A robot that can mow our lawns safely
- A car without steering wheel or pedals that can take us to places we typically go as safely as a median human driver can
- Automated theorem proving of currently problematic proofs, and not just verification
- Practical goal driven underwater robotic navigation
- A home tutor that produces a better distribution of college board exam results in students than public or private educational institutions, better meaning higher mean and lower standard deviations
Based on the seven factors already listed above plus one more, the instantaneous state of AI research and its publication during each moment of the search for probabilities regarding the above seven milestone, some probabilistic predictions can be made about 2029. The bullet items primarily driving the numbers are at the top of this answer4, 5, 6.
- < 1% — bullet item 2 too low, and 7 too skewed toward fear
- 40% — bullet item 1 too low
- 50% — bullet items 1, 2, 3, and 7 all favorable
- 2% — bullet item 2 too low, and 7 too skewed toward fear
- < 1% — bullet items 2 too high, 3 too low, and 7 too skewed toward fear
- 80% — bullet items 1 and 3
- 30% — bullet item 3 high, but 1, 2, 3, 5, and 7 are unfavorable
There are a few that some will find unpalatable. Service applications and automatic theorem provers are not at all likely to become smart in the way defined in the milestones within the next ten years. Robots will likely be swimming and assisting with mining, drilling, and troubleshooting. Level 5 automated vehicles may already be driving around town.
 All intelligent systems, including biological ones, have weaknesses and strengths, and the strengths are not perfectly reliable. For instance AI on a CAD application may select a screw fastener to attach one part to another in a sub-assembly with 100% accuracy 99.99999% of the time, seven 9s of accuracy. Much of the talk of general, strong, and weak AI fails the burden of mathematical rigor or scientific verifiability and is largely fabrication and self-deluding conjecture to get cushy, high profile jobs. When published or aired, it is done so not because of credibility but to get paid for ad impressions.
 Please don't run this experiment fully, since it would burden moderators that are volunteering to keep the sites clean. Ask the questions but do not post the answers you find. The superficiality will be obvious enough without a focus group.
 See the section The Turing Challenge to Cartesian Thought in the post Can a brain be intelligent without a body? for more information on Turing's work in this space and its limitations.
 The parenthetic (likely) in the question in the body of the question is correctly placed. The question's tag predicting-ai-milestones is also correct. The likelihoods listed will change because, as the search for likelihoods of AI milestones progresses, the eight factors listed, which are involved in the predictions, will change. This answer author may or may not change the predictions accordingly.
 The reasons behind these probabilities cannot be fully disclosed for contractual reasons, but what is disclosed is explained where it can be. Furthermore, the results of prediction are based on the information available to this particular answer author. Others may have other numerical numbers to offer based on other quantitative or qualitative information and can disclose what they wish and are legally allowed to do in another answer.
 There is no guarantee made or implied in this answer.